The problem is to factorize a list of given algebraic expressions completely.

1. Problem Description

The problem is to factorize a list of given algebraic expressions completely.

2. Solution Steps

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. $ma + 2bm + m^2$ (cannot be factorized easily.)

1

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

2

0. $ax^2 + ay + 2ab$ (cannot be factorized easily.)

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

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

3. Final Answer

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. $ma + 2bm + m^2$

1

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

2

0. $ax^2 + ay + 2ab$

2

1. $xk(x+k)$

2

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

2

3. $bc(a-3b)$

2

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

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