Find the square. Simplify your answer. (4t + 1)^2 ______

Identify Binomial and Formula: Identify the binomial to be squared and the special case formula. The given binomial is (4t + 1), and we need to find the square of this binomial. 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 (4t + 1). In the binomial (4t + 1), a is 4t and b is 1. We will use these values in the special case formula to expand the square of the binomial.Apply Special Case Formula: Apply the special case formula to expand (4t + 1)^2. Using the formula (a + b)^2 = a^2 + 2ab + b^2, we substitute a with 4t and b with 1 to get: (4t + 1)^2 = (4t)^2 + 2*(4t)*1 + 1^2Simplify Expression: Simplify the expression by performing the calculations. (4t)^2 + 2*(4t)*1 + 1^2 = 16t^2 + 8t + 1

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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

(4t + 1)^2

Identify Binomial and Formula: Identify the binomial to be squared and the special case formula. $\newline$ The given binomial is $(4t + 1)$ , and we need to find the square of this binomial. 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 $(4t + 1)$ . $\newline$ In the binomial $(4t + 1)$ , $a$ is $4t$ and $b$ is $1$ . We will use these values in the special case formula to expand the square of the binomial.
Apply Special Case Formula: Apply the special case formula to expand $(4t + 1)^2$ . Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we substitute $a$ with $4t$ and $b$ with $1$ to get: $(4t + 1)^2 = (4t)^2 + 2\cdot(4t)\cdot1 + 1^2$
Simplify Expression: Simplify the expression by performing the calculations. $\newline$ $(4t)^2 + 2\cdot(4t)\cdot1 + 1^2 = 16t^2 + 8t + 1$