Find the square. Simplify your answer. (3t + 4)^2 ______

Identify values in binomial: We are asked to find the square of the binomial (3t + 4). The square of a binomial (a + b)^2 is given by the formula a^2 + 2ab + b^2. We will apply this formula to (3t + 4)^2.Apply binomial square formula: Identify the values of a and b in the binomial (3t + 4). Here, a is 3t and b is 4.Expand (3t + 4)^2: Apply the square of a binomial formula to expand (3t + 4)^2. (3t + 4)^2 = (3t)^2 + 2(3t)(4) + 4^2Simplify each term: Simplify each term in the expansion. (3t)^2 = 9t^2 (since 3t * 3t = 9t^2) 2(3t)(4) = 24t (since 2 * 3t * 4 = 24t) 4^2 = 16 (since 4 * 4 = 16)Combine simplified terms: Combine the simplified terms to get the final answer. (3t + 4)^2 = 9t^2 + 24t + 16

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Find the square. Simplify your answer. $\newline$ $(3t + 4)^2$

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Math Problems

Algebra 1

Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(3t + 4)^2

Identify values in binomial: We are asked to find the square of the binomial $(3t + 4)$ . The square of a binomial $(a + b)^2$ is given by the formula $a^2 + 2ab + b^2$ . We will apply this formula to $(3t + 4)^2$ .
Apply binomial square formula: Identify the values of $a$ and $b$ in the binomial $(3t + 4)$ . Here, $a$ is $3t$ and $b$ is $4$ .
Expand $(3t + 4)^2$ : Apply the square of a binomial formula to expand $(3t + 4)^2.$ $(3t + 4)^2 = (3t)^2 + 2(3t)(4) + 4^2$
Simplify each term: Simplify each term in the expansion. $\newline$ $(3t)^2 = 9t^2$ (since $3t \times 3t = 9t^2$ ) $\newline$ $2(3t)(4) = 24t$ (since $2 \times 3t \times 4 = 24t$ ) $\newline$ $4^2 = 16$ (since $4 \times 4 = 16$ )
Combine simplified terms: Combine the simplified terms to get the final answer. $\newline$ $(3t + 4)^2 = 9t^2 + 24t + 16$