Question

simplify;


x^2-16x+64
------------------
x^2 - 64







Using complete sentences, explain each step in simplifying the ratio x^2+8x
and provide the simplified form. ----------
x^2+0x+16



Are 2x+4
---------
3x+6


equivalent expressions? Using complete sentences, explain why or why not.

Answer 1

the second one should look like this x^2+8x
--------
x^2-64

Answer 2

(x^(2)-16x+64)/(x^(2)-64)

Factor the trinomial x^(2)-16x+64.
((x-8)(x-8))/(x^(2)-64)

The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
((x-8)(x-8))/((x-8)(x+8))

Reduce the expression by canceling out the common factor of (x-8) from the numerator and denominator.
(x-8)/(x+8)