Factor the Following expressions Show all steps please

Question

1) 6a^5-6a^3b^2-6a^2b^3+6b^5

2) (x-y)^3+125

3) 2(a-b)^2+5(a-b)+3

4) 6x^2-13x-63? 

 

 

Answer 1

(1).

The expression is .

Answer 2

(2).

The expression is .

Apply Sum of Two Cubes : .

Answer 3

(3).

The expression is .

Answer 4

The trinomial 6x² - 13x - 63.

Multiply first term 6x² and last term - 63 = - 378x²

The correct pair of the terms - 27x and 14x multiply to - 378x² and add to - 13x.

Replace the middle term - 13x with - 27x + 14x.

= 6x² - 27x + 14x - 63

Group the terms into two pairs.

= (6x² - 27x) + (14x - 63)

Factor out 3x from the first group  and factor out 7 from the second group.

= 3x(2x - 9) + 7(2x - 9)

Factor out common term 2x - 9.

= (3x + 7)(2x - 9)

Factoring of 6x² - 13x - 63 = (3x + 7)(2x - 9).