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Shubham 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Evaluate the product without multiplying directly: 103 x 107?

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Ram Mohan replied | 21/11/2016

Their product is 11021. First add 7 to 103 OR add 3 to 107 we get 110 either way. take this 110 as left portion of our answer 110, now multiply 3 and 7, take this product 21 as right portion of the answer. 21 putting the two portions together, we get the product of 103 and 107 as 11021.

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Mamata replied | 29/11/2016

103 +3
107 +7
....................
11021
103 is 3 above base 100 and 107 is 7 above base 100
103+7=107+3=110 and multiply the deficiencies i.e 3 x 7=21.
So, 103 107=11021.

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R.s.praveen 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

If x + y = 11 and x - y = 5. (Find the value of square of x) + (square of y)?

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Tapas replied | 28/11/2016

x + y = 11, x - y = 5. Adding, we get: 2x = 16, x = 8. So, y=3.
(sq of x) + (sq of y) = (sq of 8) + (sq of 3) = 64 + 9 = 73.

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Chandan replied | 05/12/2016

x + y = 11, x - y = 5. Subtracting these two equations , we get: 2y = 6, So, y=3 and by putting this y value in any one equation we get x = 8.
(sq of x) + (sq of y) = (sq of 8) + (sq of 3) = 64 + 9 = 73.

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Abishiek 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Use suitable identities to find the product: (x + 4) (x + 10)?

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Dinnu replied | 03/12/2016

Use ( x+ a)(x+b) identity.

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Anurag 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Factorise: 9(square of x) + 6 xy + (square of y)?

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Saurabh replied | 04/12/2016

(3x)^2 + 2*3x*1 + (1y)^2
A ^2 + 2*A *B + B ^2 IDENTITY Therefore a=3x and b=y
(3x+y)(3x+y) will be the answer.

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Meera replied | 04/12/2016

(3x+y)square.

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I

Issac 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Expand the given: [square of (x + 2y + 4z)]?

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Chandan replied | 22/11/2016

(square of x) + 4(square of y) + 16(square of z) + 4xy + 16yz + 8xz

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S

S 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Expand: [cube of (2 x + 1)]?

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Saba replied | 05/12/2016

(2x+1)^3.
Formula of (a+b)^3= a^3+b^3+3ab(a+b).
So, (2x)^3+1^3+3(2x*1)(2x+1).
=8x^3+1+6x(2x+1)
=8x^3+1+12x^2+6x
=8x^2+12x^2+6x+1.

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U

Uma 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Evaluate the identity: [cube of (99)]?

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Sreedevi replied | 07/12/2016

(a-b)^3 = a^3-3a^2b+3ab^2-b^3.
(99)^3 = (100 -1)^3.

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Shambhavi replied | 07/12/2016

(a+b)^3=a3 + 3a^2b + 3ab^2 + b^3,
thus, 99^3=(100-1)^3.
Taking 100 as a, and 1 as b, we can use the formula (a+b)^3 given above to expand and get the answer.

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P

Priya 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Factorise: 8(cube of a) + (cube of b) + 12 (square of a)(b) + 6(a)(square of b)?

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Mamata replied | 24/11/2016

8a^3+b^3+12(a^2)b +6a(b^2)
= (2a)^3+(b^3)+3 x( (2a)^2) (b) + 3 x (2a) x (b^2)
= ((2a+b)^3).
Cube of (2a+b).

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S

Sk 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

If x + y + z = 0, show that: (cube of x) + (cube of y) + (cube of z) = 3xyz?

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Saba replied | 05/12/2016

We know that, a 3 + b 3 + c 3 = (a + b + c)(a 2 + b 2 + c 2 - ab - bc - ca) + 3abc.
Substitute (a + b +c) = 0 in above equation:
=> a 3 + b 3 + c 3 = 0 x (a 2 + b 2 + c 2 - ab - bc - ca) + 3abc
=>a 3 + b 3 + c 3 = 3abc.

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N

Nagarunja 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Without actually calculating the cubes, find the value of: [cube of (-12)] + [cube of (7)] + [cube of (5)]?

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Sachin replied | 27/11/2016

=3*-12*7*5
=-1260

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Sreedevi replied | 02/12/2016

The given expression is in the form of (a+b+c)^3. As on adding a,b,c we are getting 0, we can apply the formula: If a+b+c = 0 then,
(a+b+c)^3 = 3 abc; On applying the above formula, we get (-12) ^3+(7)^3+(5)^3 = 3(-12)(7)(5) = - 1260.

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C

Chandramami 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

If (square of x) + (inverse square of x) = 102, evaluate x + (inverse of x)?

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Shambhavi replied | 07/12/2016

Squaring (x+1/x) , we get, (x^2+x^-2+2), but we know that x^2+x^-2 is equal to 102, thus (x+1/x)+2=102+2=104.

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M

Manmohan 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Evaluate: (a - 0.1) (a + 0.1)?

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Neelabh Tiwari replied | 03/12/2016

Square of a - 0.01.

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Chandan replied | 05/12/2016

We know that, ( (Square of a)- (Square of b)) = (a+b)(a-b).
Hence, (Square of a - 0.01) (Ans).

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S

Saravana 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Factorise: abx + aby - bcx - bcy?

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Shambhavi replied | 07/12/2016

=(ab-bc)*x+(ab-bc)*y
=(ab-bc)(x+y)
Thus, factorized.

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Barkha replied | 07/12/2016

[abx-bcx]+[aby-bcy]
taking x and y common terms
x(ab-bc) +y(ab-bc)
(ab-bc) is common term. So,
(ab-bc) (x+y)

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M

Madhusudhan 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

If a + b + c = 0, then what is the value of [(cube of a) + (cube of b) +
(cube of c)?]

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Sachin replied | 27/11/2016

3abc.

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Chandan replied | 05/12/2016

[(cube of a) + (cube of b) + (cube of c)= 3 abc.
If a + b + c = 0.

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K

Krishna 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Write the decimal expansion for: 63. 801?

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Shikha replied | 23/11/2016

6*10+3*1+8/1+0/10+1/100.

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Mamata replied | 24/11/2016

6x(10^1)+3x(10^0) + 8 x (10^(-1)) +0x(10^(-2))+1x(10^(-3)).

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D

Divya 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Find the sum of: 5 + x - (square of x), 3x + 5 + 2(square of x)?

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Sarvajeet replied | 26/11/2016

10+ 4x + (square of x).

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Sachin replied | 27/11/2016

sq of x + 4x+10

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A

Ajit 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Subtract: 2(cube of x) - (square of x) + 4x - 6 from (cube of x) + 5(square of x) - 4x + 6?

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Chandan replied | 22/11/2016

(cube of x) + 5(square of x) - 4x + 6-[ 2(cube of x) - (square of x) + 4x - 6 from (cube of x) ] = - (cube of x) + 6(square of x) - 8x + 12

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S

Sudha 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Multiply: (ax + by) (5x + 6y)?

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Chandan replied | 22/11/2016

5a(square of x) + 6axy + 5bxy + 6b(square of y)

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A

Ashwin 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Factorise: 4(square of x) + 9(square of y) + 16(square of z) + 12xy - 24 yz - 16xz?

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M

Mayur 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Factorise: 27(cube of y) + 125(cube of z)?

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T

Trupti 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

What are the possible expressions for the dimension of the cuboids whose volumes is: 3(square of x) - 12x?

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T.v. 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Evaluate: [square of (399)]?

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Ajay 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Give the fractional expansion for: 9.764?

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D

D 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

What do you mean by expansion with respect to mathematics?

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T

Tejas 09/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Expansions

Multiply: 11 x(square of y) by -8 x(cube of y)?

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