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Find the square. Simplify your answer.

(3k+4)^(2)

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

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Multiply two binomials: special cases

Full solution

Q. Find the square. Simplify your answer.

\newline

(3 k+4)^{2}

Identify binomial and formula: Identify the binomial to be squared and the special case formula to use. $\newline$ The binomial to be squared is $(3k + 4)$ , and it is in the form of $(a + b)^2$ . $\newline$ Special case: $(a + b)^2 = a^2 + 2ab + b^2$
Identify values of $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial $(3k + 4)$ . Compare $(3k + 4)^2$ with $(a + b)^2$ . $a = 3k$ $b = 4$
Apply binomial formula: Apply the square of a binomial formula to expand $(3k + 4)^2$ . Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we get: $(3k + 4)^2 = (3k)^2 + 2(3k)(4) + 4^2$
Simplify expansion: Simplify each term in the expansion of $(3k + 4)^2$ .
$(3k)^2 + 2(3k)(4) + 4^2$
= $(3k \times 3k) + (2 \times 3 \times 4)k + (4 \times 4)$
= $9k^2 + 24k + 16$

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