Question

factor $18a^2 - 32$:
a. $2(3a + 4)(3a - 4)$
b. $2(9a + 16)^2$
c. $(3a - 4)^2$
d. $2(2a + 3)(2a - 3)$

factor $25x^2 - 16y^2$:
a. $(5x - 4y)^2$
b. not factorable
c. $(5x + 4y)(5x - 4y)$
d. $(5x + 4y)(5x + 4y)$

Explanation:

Problem 1: Factor $18a^2 - 32$

Step1: Factor out the GCF

$18a^2 - 32 = 2(9a^2 - 16)$

Step2: Apply difference of squares

$9a^2 - 16 = (3a)^2 - 4^2 = (3a+4)(3a-4)$

Step3: Combine results

$18a^2 - 32 = 2(3a+4)(3a-4)$

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Problem 2: Factor $25x^2 - 16y^2$

Step1: Recognize difference of squares

$25x^2 - 16y^2 = (5x)^2 - (4y)^2$

Step2: Apply difference of squares rule

$(5x)^2 - (4y)^2 = (5x+4y)(5x-4y)$

Answer:

1. a. $2(3a + 4)(3a - 4)$
2. c. $(5x + 4y)(5x - 4y)$