7.4 Factor Special Products

Before you get started, take this readiness quiz.

Simplify: $\left(12 x\right)^{2} .$
If you missed this problem, review the reference.

Multiply: $\left(m + 4\right)^{2} .$
If you missed this problem, review the reference.

Multiply: $\left(p - 9\right)^{2} .$
If you missed this problem, review the reference.

Multiply: $\left(k + 3\right) \left(k - 3\right) .$
If you missed this problem, review the reference.

Factor: $4 x^{2} + 12 x + 9$.

Factor: $9 y^{2} + 24 y + 16$.

Factor: $64 y^{2} - 80 y + 25$.

Factor: $16 z^{2} - 72 z + 81$.

Factor: $49 x^{2} + 84 x y + 36 y^{2}$.

Factor: $64 m^{2} + 112 m n + 49 n^{2}$.

Factor: $9 x^{2} + 50 x + 25$.

Factor: $16 r^{2} + 30 r s + 9 s^{2}$.

Factor: $9 u^{2} + 87 u + 100$.

Factor: $8 x^{2} y - 24 x y + 18 y$.

Factor: $27 p^{2} q + 90 p q + 75 q$.

Factor: $h^{2} - 81$.

Factor: $k^{2} - 121$.

Factor: $m^{2} - 1$.

Factor: $81 y^{2} - 1$.

Factor: $121 x^{2} - 49 y^{2}$.

Factor: $196 m^{2} - 25 n^{2}$.

Factor: $144 p^{2} - 9 q^{2}$.

Factor: $100 - h^{2}$.

Factor: $144 - x^{2}$.

Factor: $169 - p^{2}$.

Factor: $x^{4} - y^{4}$.

Factor: $a^{4} - b^{4}$.

Factor: $x^{4} - 16$.

Factor: $8 x^{2} y - 98 y$.

Factor: $7 x y^{2} - 175 x$.

Factor: $45 a^{2} b - 80 b$.

Factor: $6 x^{2} + 96$.

Factor: $8 a^{2} + 200$.

Factor: $36 y^{2} + 81$.

Factor: $x^{3} + 27$.

Factor: $y^{3} + 8$.

Factor: $u^{3} - 125$.

Factor: $v^{3} - 343$.

Factor: $64 - 27 x^{3}$.

Factor: $27 - 8 y^{3}$.

Factor: $8 x^{3} - 27 y^{3}$.

Factor: $1000 m^{3} - 125 n^{3}$.

Factor: $500 p^{3} + 4 q^{3}$.

Factor: $432 c^{3} + 686 d^{3}$.

Factor.

$16 y^{2} + 24 y + 9$

Factor.

$36 s^{2} + 84 s + 49$

Factor.

$100 x^{2} - 20 x + 1$

Factor.

$25 n^{2} - 120 n + 144$

Factor.

$49 x^{2} - 28 x y + 4 y^{2}$

Factor.

$25 n^{2} + 25 n + 4$

Factor.

$64 m^{2} - 16 m + 1$

Factor.

$10 k^{2} + 80 k + 160$

Factor.

$75 u^{3} - 30 u^{2} v + 3 u v^{2}$

Factor.

$x^{2} - 16$

Factor.

$25 v^{2} - 1$

Factor.

$121 x^{2} - 144 y^{2}$

Factor.

$169 c^{2} - 36 d^{2}$

Factor.

$4 - 49 x^{2}$

Factor.

$16 z^{4} - 1$

Factor.

$5 q^{2} - 45$

Factor.

$24 p^{2} + 54$

Factor.

$x^{3} + 125$

Factor.

$z^{3} - 27$

Factor.

$8 - 343 t^{3}$

Factor.

$8 y^{3} - 125 z^{3}$

Factor.

$7 k^{3} + 56$

Factor.

$2 - 16 y^{3}$

Factor.

$64 a^{2} - 25$

Factor.

$27 q^{2} - 3$

Factor.

$16 x^{2} - 72 x + 81$

Factor.

$8 p^{2} + 2$

Factor.

$125 - 8 y^{3}$

Factor.

$45 n^{2} + 60 n + 20$

Landscaping Sue and Alan are planning to put a 15 foot square swimming pool in their backyard. They will surround the pool with a tiled deck, the same width on all sides. If the width of the deck is w, the total area of the pool and deck is given by the trinomial $4 w^{2} + 60 w + 225$. Factor the trinomial.

Why was it important to practice using the binomial squares pattern in the chapter on multiplying polynomials?

Explain why $n^{2} + 25 \neq \left(n + 5\right)^{2}$. Use algebra, words, or pictures.