To find the value of x2−15x2−51 at x=−1x=−1, substitute x=−1x=−1 into the expression:

(−1)2−15(−1)2−51

1−151−51

To combine the terms with a common denominator, express 1 as 5555:

55−1555−51

4554

So, the value of x2−15x2−51 at x=−1x=−1 is 4554.

To find the value of x2+y2−10x2+y2−10 at x=0x=0 and y=0y=0, substitute these values into the expression:

(0)2+(0)2−10(0)2+(0)2−10

0+0−100+0−10

−10−10

So, the value of x2+y2−10x2+y2−10 at x=0x=0 and y=0y=0 is −10−10.

To simplify the expression (a+b+c)(a+b−c)(a+b+c)(a+b−c), you can use the distributive property (FOIL method):

(a+b+c)(a+b−c)(a+b+c)(a+b−c)

=a(a+b−c)+b(a+b−c)+c(a+b−c)=a(a+b−c)+b(a+b−c)+c(a+b−c)

Now, distribute each term:

=a2+ab−ac+ba+b2−bc+ca+cb−c2=a2+ab−ac+ba+b2−bc+ca+cb−c2

Combine like terms:

=a2+2ab−ac+b2−bc−c2=a2+2ab−ac+b2−bc−c2

So, the simplified form of (a+b+c)(a+b−c)(a+b+c)(a+b−c) is a2+2ab−ac+b2−bc−c2a2+2ab−ac+b2−bc−c2.

To evaluate the product 8.56×11.608.56×11.60, you can simply multiply the two numbers:

8.56×11.60=99.5368.56×11.60=99.536

So, 8.56×11.608.56×11.60 is equal to 99.53699.536.

To evaluate (95)2(95)2 using identities, you can use the square of a binomial formula:

(a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2

In this case, a=90a=90 and b=5b=5. Apply the formula:

(95)2=(90+5)2(95)2=(90+5)2

=902+2×90×5+52=902+2×90×5+52

=8100+900+25=8100+900+25

=9025=9025

So, (95)2(95)2 is equal to