Grade 10 factoring help?

Question

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
Textbook Answer: x(x+y) (x-y) (x^2+1)

Q2: x^3 + 5x^2 + 6x + x^2y +5xy +6y
Textbook Answer: (x+y) (x+3) (x+2)

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

Answer 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).

Answer 2

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).

Answer 3

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).

Answer 4

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)].