Question

factor $16m^{4}-100n^{4}$:

a. $4(2m^{2}+5n^{2})(2m^{2}-5n^{2})$

b. $4(4m^{2}+3n^{2})(4m^{2}-3n^{2})$

c. $4(3m^{2}+4n^{2})(3m^{2}-4n^{2})$

d. $4(2m^{2}+25n^{2})^{2}$

Explanation:

Step1: Factor out GCF

Identify GCF of $16m^4$ and $100n^4$ is 4:
$16m^4 - 100n^4 = 4(4m^4 - 25n^4)$

Step2: Recognize difference of squares

Rewrite $4m^4-25n^4$ as $(2m^2)^2-(5n^2)^2$:
$4[(2m^2)^2 - (5n^2)^2]$

Step3: Apply difference of squares rule

Use $a^2-b^2=(a+b)(a-b)$:
$4(2m^2+5n^2)(2m^2-5n^2)$

Answer:

a. $4(2m^{2}+5n^{2})(2m^{2}-5n^{2})$