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Practice Solutions

Factor out the GCF.

$5 x^{2} + 35 x + 5$
$5 (x^{2} + 7 x + 1)$

$14 x^{3} y - 8 x y$
$2 x y (7 x^{2} - 4)$

Factor by grouping.

$3 x^{2} - 5 x + 6 x y - 10 y$
$(3 x^{2} - 5 x) + (6 x y - 10 y) x (3 x - 5) + 2 y (3 x - 5) (3 x - 5) (x + 2 y)$

$10 x^{2} z + 12 x z - 15 x - 18$
$(10 x^{2} z + 12 x z) + (- 15 x - 18) 2 x z (5 x + 6) - 3 (5 x + 6) (5 x + 6) (2 x z - 3)$

Factor the perfect square trinomial.

$x^{2} + 22 x + 121$
$(x + 11) (x + 11) {(x + 11)}^{2}$

$4 x^{2} + 20 x + 25$
$(2 x + 5) (2 x + 5) {(2 x + 5)}^{2}$

Factor the difference of two squares.

$4 x^{2} - 25$
$(2 x - 5) (2 x + 5)$

$100 x^{2} - 49 y^{2}$
$(10 x + 7 y) (10 x - 7 y)$

Factor.

$12 x^{2} y^{3} - 14 x y^{2} + 18 x y$
$2 x y (6 x y^{2} - 7 y + 9)$

$100 x^{4} + 225 x^{2} + 4 x^{2} y^{2} + 9 y^{2}$
$25 x^{2} (4 x^{2} + 9) + y^{2} (4 x^{2} + 9) (25 x^{2} + y^{2}) (4 x^{2} + 9)$

Note

The solution is the sum of squares and cannot be factored further.

$9 w^{2} + 30 w + 25$
$(3 w + 5) (3 w + 5) {(3 w + 5)}^{2}$

$6 x y + 4 x + 9 y + 6$
$2 x (3 y + 2) + 3 (3 y + 2) (2 x + 3) (3 y + 2)$

$225 x^{2} y^{2} - 196 w^{2}$
$(15 x y - 14 w) (15 x y + 14 w)$

$49 g h^{2} - 21 g^{2} h + 7 g h$
$7 g h (7 h - 3 g + 1)$

$a^{2} - 2 a b + b^{2}$
$(a - b) (a - b) {(a - b)}^{2}$

$a^{2} - b^{2}$
$(a + b) (a - b)$