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

Identify binomial and formula: Identify the binomial to be squared and the special case formula to use. The binomial to be squared is (2t + 2), and it is in the form of (a + b)^2. Special case: (a + b)^2 = a^2 + 2ab + b^2Determine values of a and b: Determine the values of a and b in the binomial (2t + 2). Comparing (2t + 2) with (a + b), we find that a = 2t and b = 2.Apply binomial square formula: Apply the square of a binomial formula to expand (2t + 2)^2. Using the formula (a + b)^2 = a^2 + 2ab + b^2, we get: (2t + 2)^2 = (2t)^2 + 2(2t)(2) + 2^2Simplify expression: Simplify the expression (2t)^2 + 2(2t)(2) + 2^2. (2t)^2 + 2(2t)(2) + 2^2 = (2t * 2t) + (2 * 2 * 2)t + 2 * 2 = 4t^2 + 8t + 4

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

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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

(2t + 2)^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 $(2t + 2)$ , and it is in the form of $(a + b)^2$ . $\newline$ Special case: $(a + b)^2 = a^2 + 2ab + b^2$
Determine values of $a$ and $b$ : Determine the values of $a$ and $b$ in the binomial $(2t + 2)$ . Comparing $(2t + 2)$ with $(a + b)$ , we find that $a = 2t$ and $b = 2$ .
Apply binomial square formula: Apply the square of a binomial formula to expand $(2t + 2)^2$ . Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we get: $(2t + 2)^2 = (2t)^2 + 2(2t)(2) + 2^2$
Simplify expression: Simplify the expression $(2t)^2 + 2(2t)(2) + 2^2.$ $(2t)^2 + 2(2t)(2) + 2^2$ $= (2t \cdot 2t) + (2 \cdot 2 \cdot 2)t + 2 \cdot 2$ $= 4t^2 + 8t + 4$