Simplify fully the following expressions by combining the like terms. 9(2x − t) + 23xt + x(−4 + 5t)

Simplify fully the following expressions by combining the like terms.

9(2x − t) + 23xt + x(−4 + 5t)

Solutions

Expert Solution

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

9(2x + −t) + 23xt + x(−4 + 5t)

we use the distributive property of multiplication on the first term.

[9(2x + −t) = 9 · 2x + 9 · −t]

we use the rules for multiplying signed terms. [9 · 2x + 9 · −t = 18x + −9t]

Use the distributive property of multiplication on the third term.

[x(−4 + 5t) = x · −4 + x · 5t]

Use the rules for multiplying signed terms. [x · −4 + x · 5t = −4x + 5xt]

Substitute the results into the expression. (18x + −9t) + 23xt + (−4x + 5xt)

Remove the parentheses. 18x + −9t + 23xt + −4x + 5xt

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

18x + −4x + −18t + 23xt + 5xt

Use the associative property for addition.

(18x + −4x) + −9t + (23xt + 5xt)

we combine like terms using addition rules for signed numbers.

(14x) + −9t + (28xt)

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

14x − +9t + 28xt

14x − 9t + 28xt

the simplified expression is 14x − 9t + 28xt

joseph irungu answered 2 years ago

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