Question

factor completely

1. 400-25y²
2. x³+x²+x+1
3. x⁶-7x³-8
4. 16m²-56mn+49n²
5. (x²+1)^-1/2(x-7)²(x²+1)^1/2(x-7)

Answer 1

1.

$$400-25y^2=25(16-y^2)=25(4-y)(4+y)$$

2.

$$x^3+x^2+x+1=x^2(x+1)+(x+1)$$

$$=(x+1)(x^2+1)$$

3.

$$x^6-7x^3-8=(x^3+1)(x^3-8)$$

$$=(x+1)(x-2)(x^2-x+1)(x^2+2x+4)$$

4.

$$16m^2-56mn+49n^2=(4m-7n)^2$$

5.

$$(x^2+1)^{-1/2}(x-7)^2(x^2+1)^{1/2}(x-7)$$

$$=(x-7)^3$$