The problem asks us to factorize the given expressions completely.

1. Problem Description

The problem asks us to factorize the given expressions completely.

2. Solution Steps

Here are the factorizations of each expression:

1. $5a + 5b = 5(a+b)$

2. $7x + 7y = 7(x+y)$

3. $7x + x^2 = x(7+x)$

4. $y^2 + 8y = y(y+8)$

5. $2y^2 + 3y = y(2y+3)$

6. $6y^2 - 4y = 2y(3y-2)$

7. $3x^2 - 21x = 3x(x-7)$

8. $16a - 2a^2 = 2a(8-a)$

9. $6c^2 - 21c = 3c(2c-7)$

1

0. $15x - 9x^2 = 3x(5-3x)$

1

1. $56y - 21y^2 = 7y(8-3y)$

1

2. $ax + bx + 2cx = x(a+b+2c)$

1

3. $x^2 + xy + 3xz = x(x+y+3z)$

1

4. $x^2y + y^3 + z^2y = y(x^2 + y^2 + z^2)$

1

5. $3a^2b + 2ab^2 = ab(3a+2b)$

1

6. $x^2y + xy^2 = xy(x+y)$

1

7. $6a^2 + 4ab + 2ac = 2a(3a+2b+c)$

1

8. $ma + 2bm + m^2 = m(a+2b+m)$

1

9. $2kx + 6ky + 4kz = 2k(x+3y+2z)$

2

0. $ax^2 + ay + 2ab = a(x^2 + y + 2b)$

2

1. $x^2k + xk^2 = xk(x+k)$

2

2. $a^3b + 2ab^2 = ab(a^2+2b)$

2

3. $abc - 3b^2c = bc(a-3b)$

2

4. $2a^2e - 5ae = ae(2a-5)$

2

5. $a^3b + ab^3 = ab(a^2 + b^2)$

2

6. $x^3y + x^2y^2 = x^2y(x+y)$

2

7. $6xy^2 - 4x^2y = 2xy(3y-2x)$

2

8. $3ab^3 - 3a^3b = 3ab(b^2-a^2) = 3ab(b-a)(b+a)$

2

9. $2a^3b + 5a^2b^2 = a^2b(2a+5b)$

3

0. $ax^2y - 2ax^2z = ax^2(y-2z)$

3

1. $2abx + 2ab^2 + 2a^2b = 2ab(x+b+a)$

3

2. $ayx + yx^3 - 2y^2x^2 = yx(a + x^2 - 2yx)$

3. Final Answer

The factorizations are as follows:

1. $5(a+b)$

2. $7(x+y)$

3. $x(7+x)$

4. $y(y+8)$

5. $y(2y+3)$

6. $2y(3y-2)$

7. $3x(x-7)$

8. $2a(8-a)$

9. $3c(2c-7)$

1

0. $3x(5-3x)$

1

1. $7y(8-3y)$

1

2. $x(a+b+2c)$

1

3. $x(x+y+3z)$

1

4. $y(x^2 + y^2 + z^2)$

1

5. $ab(3a+2b)$

1

6. $xy(x+y)$

1

7. $2a(3a+2b+c)$

1

8. $m(a+2b+m)$

1

9. $2k(x+3y+2z)$

2

0. $a(x^2 + y + 2b)$

2

1. $xk(x+k)$

2

2. $ab(a^2+2b)$

2

3. $bc(a-3b)$

2

4. $ae(2a-5)$

2

5. $ab(a^2 + b^2)$

2

6. $x^2y(x+y)$

2

7. $2xy(3y-2x)$

2

8. $3ab(b-a)(b+a)$

2

9. $a^2b(2a+5b)$

3

0. $ax^2(y-2z)$

3

1. $2ab(x+b+a)$

3

2. $yx(a + x^2 - 2yx)$