Evaluate expression $6 x^{2} + 6 x - 2 x^{2} - 4 x + 8 x$ by collecting the like terms together.

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Solution

Given expression: $6 x^{2} + 6 x - 2 x^{2} - 4 x + 8 x$

The like terms that involve variable $x^{2}$ are $6 x^{2} and - 2 x^{2}$ .

The like terms that involve variable $x$ are $6 x, - 4 x,$ and $8 x$ .

By adding the like terms that involve variable $x^{2}$ , we get:
$5 x^{2} - 2 x^{2} = 4 x^{2}$

$∴ 5 x^{2} - 2 x^{2} = 4 x^{2}$

By adding the like terms that involve variable $x$ , we get:
$6 x - 4 x - ------- - + 8 x = 2 x + 8 x = 10 x$

Simplification of the given expression would be obtained by adding the like terms that involve $x^{2}$ and $x$ .

$6 x^{2} + 6 x - 2 x^{2} - 4 x + 8 x$

$= 6 x^{2} - 2 x^{2} - --------- - + 6 x - 4 x + 8 x - ------------ -$

$= 4 x^{2} + 10 x$

$∴ 6 x^{2} + 6 x - 2 x^{2} - 4 x + 8 x = 4 x^{2} + 10 x$

As a result, expression $6 x^{2} + 6 x - 2 x^{2} - 4 x + 8 x$ would become $4 x^{2} + 10 x$ after simplification.

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