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Complete the Area Model that would be used to multiply $\newline$ $3x(x^{2}+4x+5)$ $\newline$ by dragging the responses to the correct location. $\newline$ Some parts have already been filled out for you. $\newline$ $3x^{3}$ $\newline$ $3x^{2}$ $\newline$ $x^{2}$ $\newline$ $x$ $\newline$ $4x$ $\newline$ $4$ $\newline$ $15x$ $\newline$ $15$

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Sine and cosine of complementary angles

Full solution

Q. Complete the Area Model that would be used to multiply

\newline

3x(x^{2}+4x+5)

\newline

by dragging the responses to the correct location.

\newline

Some parts have already been filled out for you.

\newline

3x^{3}

\newline

3x^{2}

\newline

x^{2}

\newline

x

\newline

4x

\newline

4

\newline

15x

\newline

15

Given Expression: We are given the expression $3x(x^2 + 4x + 5)$ and need to complete the Area Model. The Area Model is a visual representation of the distributive property of multiplication. We will multiply each term in the parenthesis by $3x$ .
Multiply by $x^2$ : First, multiply $3x$ by $x^2$ . This gives us $3x^3$ , which is already filled out in the Area Model. $\newline$ $3x \times x^2 = 3x^3$
Multiply by $4x$ : Next, multiply $3x$ by $4x$ . This gives us $12x^2$ . We place this term in the Area Model next to $3x^3$ . $\newline$ $3x \times 4x = 12x^2$
Multiply by $5$ : Finally, multiply $3x$ by $5$ . This gives us $15x$ . We place this term in the Area Model next to $12x^2$ . $\newline$ $3x \times 5 = 15x$
Complete Area Model: Now, we have all the terms needed to complete the Area Model. The terms are $3x^3$ , $12x^2$ , and $15x$ . We place them in the Area Model to represent the product of $3x(x^2 + 4x + 5)$ .

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