Question

simplify the given expression using factors

1. 5(x^2+4)^4(2x)(x-2)^4+(x^2+4)^5(4)(x-2)^3

2. (x^2+3)^(-1/3)-2/3x^2(x^2+3)^(-4/3)

3. 2x(x+6)^4-x^2(4)(x+6)^3/(x+6)^8

4. (7-3x)^1/2+3/2x(7-3x)^(-1/2)/7-3x

Answer 1

come on - this is Algebra I; no problem for a calculus student, right?

5(x^2+4)^4(2x)(x-2)^4+(x^2+4)^5(4)(x-2)^3
= 2(x^2+4)^4 (x-2)^3 (5(x-2)x + (x^2+4)2)
= 2(x^2+4)^4 (x-2)^3 (7x^2-10x+8)

now take a stab at the others. Look for common factors, one by one. Factor out the lowest powers of those that are repeated.