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Sivaraj

Mathematics Tutor

5+x-x² & 3x+5+2x² write the like terms in order, (5+5)+(x+3x)+(-x²+2x²)=10+4x+x²
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Vimala R.

Maths Teacher

103 x 107 = (100 + 3)(100 + 7) We know that (x + a)(x + b) = x^2 + (a + b)x + ab Therefore, 103 x 107 = 100^2 + (3 + 7) x 100 + 3 x 7 = 10000 + 1000 + 21 = 11021
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If x + y = 11 and x - y = 5. (Find the value of square of x) + (square of y)?

Tapas Bhattacharya

Tutor

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

Saba A.

Tuition at its Best

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

Sreedevi A.

Teacher

(a-b)^3 = a^3-3a^2b+3ab^2-b^3. (99)^3 = (100 -1)^3.
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If x + y + z = 0, show that: (cube of x) + (cube of y) + (cube of z) = 3xyz?

Saba A.

Tuition at its Best

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

Shambhavi S.

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

Chandan Singh

Tutor

We know that, ( (Square of a)- (Square of b)) = (a+b)(a-b). Hence, (Square of a - 0.01) (Ans).
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Factorise: abx + aby - bcx - bcy?

Shambhavi S.

=(ab-bc)*x+(ab-bc)*y =(ab-bc)(x+y) Thus, factorized.
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If a + b + c = 0, then what is the value of [(cube of a) + (cube of b) + (cube of c)?]

Chandan Singh

Tutor

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