Simplify each expression:
1) (x+8)^2 = x^2 + 64
2) (x-2)^3 = x^3 - 8
So for (x+8)^2 i would use a^2 + 2ab + b^2 and a would be 8 but what is b? Would it be 64?
both your answers are incorrect
why don't you apply the definition of (x+8)^2 and expand it?
(x+8)^2
= (x+8)(x+8)
= x^2 + 8x + 8x + 64
= x^2 + 16x + 64
the expression a^2 + 2ab + b^2 is (a+b)^2
so in your case a=x and b=8
Notice that this produces my answer.
for (x-2)^3 I suggest you do
(x-2)(x-2)(x-2)
= (x-2)(x^2 -4x+4)
to get a final answer of
x^3 + 6x^2 + 12x - 8
in general (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
if you let a=x and b=-2 this will produce my answer above.
Thank you!!
In the expression (x+8)^2, we can expand it using the formula (a+b)^2 = a^2 + 2ab + b^2.
In this case, "a" would be "x" and "b" would be "8". So applying the formula, we get:
(x+8)^2 = x^2 + 2(x)(8) + 8^2 = x^2 + 16x + 64.
Therefore, the simplified expression is x^2 + 16x + 64, not x^2 + 64 as you mentioned.