Question

factor $16m^2 - 9$:
a. $(4m + 3)(4m - 3)$
b. $(4m + 9)^2$
c. $(2m + 5)(2m - 5)$
d. $(3m + 4)(3m - 4)$

factor $25x^4 - 9y^4$.
a. not factorable
b. $(2x^2 + 5y^2)(2x^2 - 5y^2)$
c. $(25x^2 + 9y^2)^2$
d. $(5x^2 + 3y^2)(5x^2 - 3y^2)$

Explanation:

Step1: Recognize difference of squares

$16m^2 - 9 = (4m)^2 - 3^2$

Step2: Apply difference of squares formula

$a^2 - b^2=(a+b)(a-b)$, so $(4m)^2 - 3^2=(4m+3)(4m-3)$

Step3: Recognize difference of squares

$25x^4 - 9y^4 = (5x^2)^2 - (3y^2)^2$

Step4: Apply difference of squares formula

$a^2 - b^2=(a+b)(a-b)$, so $(5x^2)^2 - (3y^2)^2=(5x^2+3y^2)(5x^2-3y^2)$

Answer:

1. a. $(4m + 3)(4m - 3)$
2. d. $(5x^{2} + 3y^{2})(5x^{2} - 3y^{2})$