Have a factoring test but having a lot of trouble.
Here are some questions that I find difficult. I looked at the back after I gave up but even then didn't know how the answer was calculated. So a step by step thing would be appreciated.

Q1: x^5 - x^3y^2 + x^3 = xy^2

Q2: x^3 + 5x^2 + 6x + x^2y +5xy +6y

Q3: 25a^2/64 - 9b^2/49
Textbook Answer: (5a/8 - 3b/7) (5a/8 + 3b/7)

+1 vote

x5 - x3y2 + x3 - xy2

x3(x2 - y2) + x(x2 - y2)

Take out common term x2 - y2

(x2 - y2)(x3 + x)

(x2 - y2)x(x2 + 1)

Take out common term x

(x - y)(x + y)x(x2 + 1)

x(x + y)(x - y)(x2 + 1).

+1 vote

1.

x5 - x3y2 + x3 - xy2

x3(x2 - y2) + x(x2 - y2)

Take out common term x2 - y2

(x2 - y2)(x3 + x)

(x2 - y2)x(x2 + 1)

Take out common term x

(x - y)(x + y)x(x2 + 1)

x(x + y)(x - y)(x2 + 1).

+1 vote

2.

x3 + 5x2 + 6x + x2y + 5xy + 6y

Take out common term x and y

x(x2 + 5x + 6) + y(x2 + 5x + 6)

Take out common term x2 + 5x + 6

(x2 + 5x + 6)(x + y)

(x + y)(x2 + 3x + 2x + 6)

(x + y)(x(x + 3) + 2(x + 3))

(x + y)(x + 3)(x + 2).

+1 vote

3.

25a^2 / 64 - 9b^2 / 49

(5a / 8)^2 - (3b / 7)^2

Recall : Algebra  formulas a^2 - b^2 = (a - b)(a + b)

[(5a / 8) - (3b / 7)][(5a / 8) + (3b / 7)].