SIMPLIFYING ALGEBRAIC EXPRESSIONS

Problem 1 :

(4x + 7x)3

Solution :

= (4x + 7x)3

Distributing 3,

= [4x(3) + 7x(3)]

= 12x + 21x

= 33x

Problem 2 :

12z – 5z + 9z²

Solution :

= 12z – 5z + 9z²

= 7z + 9z²

Factoring z,

= 9z² + 7z

= z(9z + 7)

Problem 3 :

-7(-6m + 11m)

Solution :

= -7(-6m + 11m)

= -7(5m)

= -35m

Problem 4 :

4(11 – 3x)

Solution :

= 4(11 – 3x)

Distributing 4,

= 4(11) + 4(-3x)

= 44 – 12x

= -12x + 44

Problem 5 :

-5(5a – 3b - 6)

Solution :

= -5(5a – 3b - 6)

Distributing -5, 

= -5(5a) -5(-3b) -5(-6)

= -25a + 15b +30

Problem 6 :

-2(x² - 8x + 3x³ - 6)

Solution :

= -2(x² - 8x + 3x³ - 6)

= -2(x²) - 2(-8x) - 2(3x³) - 2(-6)

= -2x² +16x – 6x³ + 12

= -6x³ - 2x² + 16x + 12

Problem 7 :

9x – 4(6 – 3x)

Solution :

= 9x – 4(6) -4(-3x)

= 9x – 24 + 12x

combining like terms,

= 21x - 24

Problem 8 :

 5(3b – 2a) – 7b

Solution :

= 5(3b) + 5(-2a) – 7b

= 15b – 10a -7b

combining like terms,

= -10a +15b – 7b

= -10a + 8b

Problem 9 :

12 + 3(7x + 2)

Solution :

= 12 + 3(7x) + 3(2)

= 12 + 21x + 6

= 21x + 18

Problem 10 :

6(4y + 3z) – 11z

Solution :

= 6(4y) + 6(3z) – 11z

= 24y + 18z – 11z

= 24y – 7z

Problem 11 :

5 + 2(4m – 7n) + 9n

Solution :

= 5 + 2(4m) + 2(-7n) + 9n

= 5 + 8m – 14n + 9n

= 5 + 8m - 5n

Problem 12 :

12 – 7(3 – 5r) + 8r

Solution :

= 12 – 7(3) -7(-5r) + 8r

= 12 – 21 + 35r + 8r

= -9 + 43r