Question

Factorize each of the following expression:
a⁴ − 16(b − c)⁴

Answer 1

$$a^4-16(b-c{)}^4$$
$$=(a^2{)}^2-[4(b-c{)}^2{]}^2$$
$$=[a^2+4(b-c{)}^2][a^2-4(b-c{)}^2]$$
$$=[a^2+4(b-c{)}^2]a^2-[2(b-c){]}^2$$
$$=[a^2+4(b-c{)}^2][a+2(b-c)][a-2(b-c)]$$
$$=[a^2+4(b-c{)}^2](a+2b-2c)(a-2b+2c)$$