Question

(b+2)^2(b-2)^2 ___________ 32b

Answer 1

= (b²+4b+4) × (b²-4b+4)
_________________= b⁴-8b+16
________

32b
32b

Answer 2

To simplify the expression $(b+2)^2(b-2)^2 / 32b$, let's start by expanding both the numerator and denominator:

Numerator: $(b+2)^2(b-2)^2 = [(b+2)(b+2)][(b-2)(b-2)]$ Using the formula $(a+b)^2 = a^2 + 2ab + b^2$, we can simplify further: $(b+2)^2(b-2)^2 = [b^2 + 2(2)b + 2^2][b^2 - 2(2)b + 2^2]$ $(b+2)^2(b-2)^2 = [b^2 + 4b + 4][b^2 - 4b + 4]$

Denominator: $32b = 32 \cdot b$

Now, let's rewrite the expression with the expanded forms:

$\frac{(b+2)^2(b-2)^2}{32b} = \frac{[b^2 + 4b + 4][b^2 - 4b + 4]}{32b}$

Now, we can cancel out common factors between the numerator and the denominator. Both the numerator terms have a common factor of $(b^2 + 4b + 4)$:

$\frac{(b+2)^2(b-2)^2}{32b} = \frac{(b^2 + 4b + 4)(b^2 - 4b + 4)}{32b}$ $= \frac{(b^2 + 4b + 4) \cdot (b^2 - 4b + 4)}{32b}$

Next, we can attempt to factor the denominator. 32 and b have no common factors, so the denominator remains as it is.

Now, the simplified expression is:

$\frac{(b+2)^2(b-2)^2}{32b} = \frac{(b^2 + 4b + 4) \cdot (b^2 - 4b + 4)}{32b}$