Question

Simplify the following expression by combining like terms and give your answer.

8(2a − b − 3c) + 3(2a − b) − 4(6 − b)

Answer 1

we Change subtraction to addition and the sign of the terms that follow.

8(2a + −b + −3c) + 3(2a + −b) + −4(6 + −b)

Use the distributive property of multiplication on the first term.

[8(2a + −b + −3c) = 8 · 2a + 8 · −b + 8 · −3c]

Use the rules for multiplying signed terms.

[8 · 2a + 8 · −b + 8 · −3c = 16a + −8b + −24c]

Use the distributive property of multiplication on the second term.

[3(2a + −b) = 3 · 2a + 3 · −b]

Use the rules for multiplying signed terms. [3 · 2a + 3 · −b = 6a + −3b]

Use the distributive property of multiplication in the third term.

[−4(6 + −b) = −4 · 6 + −4 · −b]

Use the rules for multiplying signed terms. [−4 · 6 + −4 · −b = −24 + +4b]

we Substitute the results into the expression.

(16a + −8b + −24c) + (6a + −3b) + (−24 + +4b)

Remove the parentheses. 16a + −8b + −24c + 6a + −3b + −24 + +4b

Use the commutative property of addition to move like terms together.

16a + 6a + −8b + −3b + +4b + −24c + −24

Use the associative property for addition.

(16a + 6a) + (−8b + −3b + +4b) + −24c + −24

Combine like terms using addition rules for signed numbers.

(22a) + (−7b) + −24c + −24

Adding a negative term is the same as subtracting a positive term.

we obtain the final answer as:

22a − 7b − 24c − 24

we obtain the answer as 22a − 7b − 24c − 24