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Factorize the following. $x(x+5) +2(x+6)$

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Solve equations with the distributive property

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Q. Factorize the following.

x(x+5) +2(x+6)

Distribute $x$ into $(x+5)$ : First, distribute the $x$ into $(x+5)$ . $x\times x + x\times 5 = x^2 + 5x$
Distribute $2$ into $(x+6)$ : Now, distribute the $2$ into $(x+6)$ . $2\times x + 2\times 6 = 2x + 12$
Add distribution results: Add the results of the distributions together. $x^2 + 5x + 2x + 12$
Combine like terms: Combine like terms $5x$ and $2x$ . $\newline$ $x^2 + 7x + 12$
Factorize $x^2 + 7x + 12$ : Now, we need to factorize $x^2 + 7x + 12$ . Look for two numbers that multiply to $12$ and add up to $7$ . The numbers are $3$ and $4$ .
Write factorized form: Write the factorized form using the numbers $3$ and $4$ . $(x + 3)(x + 4)$

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