QuestionSimplify the expression: $3(x^{2}+2x+5)+2(x^{2}+3x+2)$ .

Studdy Solution

STEP 1

Assumptions1. The algebraic expression is $3\left(x^{}+ x+5\right)+\left(x^{}+3 x+\right)$ . We need to simplify the expression by performing the indicated operations and combining like terms.

STEP 2

First, distribute the numbers outside the parentheses to each term inside the parentheses.
$\left(x^{2}+2 x+5\right) =x^{2}+6x+15$ $2\left(x^{2}+ x+2\right) =2x^{2}+6x+4$

STEP 3

Now, we have two simplified expressions.
$3x^{2}+6x+15$ $2x^{2}+6x+$

STEP 4

Add these two expressions together.
$3x^{2}+6x+15 +2x^{2}+6x+4$

STEP 5

Combine like terms.
$3x^{2} +2x^{2} +x +x +15 +4$

STEP 6

Perform the addition to get the simplified expression.
$5x^{2} +12x +19$ So, the simplified form of the given algebraic expression is $5x^{2} +12x +19$ .

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