Find the square. Simplify your answer. (3q + 3)^2 ______

Identify Binomial and Formula: Identify the binomial to be squared and the special case formula to use. The given binomial is (3q + 3), and we need to square it. The special case formula for the square of a binomial (a + b)^2 is a^2 + 2ab + b^2.Identify a and b: Identify the values of a and b in the binomial. In the binomial (3q + 3), a is 3q and b is 3.Apply Binomial Formula: Apply the square of a binomial formula to expand (3q + 3)^2. Using the formula (a + b)^2 = a^2 + 2ab + b^2, we get: (3q + 3)^2 = (3q)^2 + 2(3q)(3) + (3)^2Simplify Each Term: Simplify each term in the expansion. (3q)^2 = 9q^2 (since 3q * 3q = 9q^2) 2(3q)(3) = 18q (since 2 * 3q * 3 = 18q) (3)^2 = 9 (since 3 * 3 = 9)Combine Simplified Terms: Combine the simplified terms to get the final answer. (3q + 3)^2 = 9q^2 + 18q + 9

Home

Math Problems

Algebra 1

Multiply two binomials: special cases

Full solution

Q. Find the square. Simplify your answer.

\newline

(3q + 3)^2

Identify Binomial and Formula: Identify the binomial to be squared and the special case formula to use. $\newline$ The given binomial is $(3q + 3)$ , and we need to square it. The special case formula for the square of a binomial $(a + b)^2$ is $a^2 + 2ab + b^2$ .
Identify $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial. In the binomial $(3q + 3)$ , $a$ is $3q$ and $b$ is $3$ .
Apply Binomial Formula: Apply the square of a binomial formula to expand $(3q + 3)^2$ . Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we get: $(3q + 3)^2 = (3q)^2 + 2(3q)(3) + (3)^2$
Simplify Each Term: Simplify each term in the expansion. $\newline$ $(3q)^2 = 9q^2$ (since $3q \times 3q = 9q^2$ ) $\newline$ $2(3q)(3) = 18q$ (since $2 \times 3q \times 3 = 18q$ ) $\newline$ $(3)^2 = 9$ (since $3 \times 3 = 9$ )
Combine Simplified Terms: Combine the simplified terms to get the final answer. $\newline$ $(3q + 3)^2 = 9q^2 + 18q + 9$