Find the square. Simplify your answer. (4v - 1)^2 ______

Identify values: Identify the values of a and b in the binomial (4v - 1)^2. Here, a = 4v and b = 1.Apply binomial formula: Apply the square of a binomial formula to expand (4v - 1)^2. Using the identity (a - b)^2 = a^2 - 2ab + b^2, we get: (4v - 1)^2 = (4v)^2 - 2*(4v)*1 + 1^2.Simplify terms: Simplify each term in the expansion. (4v)^2 = 16v^2 (since 4v * 4v = 16v^2), -2*(4v)*1 = -8v (since 2 * 4v * 1 = 8v), 1^2 = 1 (since 1 * 1 = 1).Combine for final answer: Combine the simplified terms to get the final answer. (4v - 1)^2 = 16v^2 - 8v + 1.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the square. Simplify your answer. $\newline$ $(4v - 1)^2$

View step-by-step help

Home

Math Problems

Algebra 1

Multiply two binomials: special cases

Full solution

Q. Find the square. Simplify your answer.

\newline

(4v - 1)^2

Identify values: Identify the values of $a$ and $b$ in the binomial $(4v - 1)^2$ . Here, $a = 4v$ and $b = 1$ .
Apply binomial formula: Apply the square of a binomial formula to expand $(4v - 1)^2$ . Using the identity $(a - b)^2 = a^2 - 2ab + b^2$ , we get: $(4v - 1)^2 = (4v)^2 - 2\cdot(4v)\cdot1 + 1^2$ .
Simplify terms: Simplify each term in the expansion. $\newline$ $(4v)^2 = 16v^2$ (since $4v \times 4v = 16v^2$ ), $\newline$ $-2\times(4v)\times1 = -8v$ (since $2 \times 4v \times 1 = 8v$ ), $\newline$ $1^2 = 1$ (since $1 \times 1 = 1$ ).
Combine for final answer: Combine the simplified terms to get the final answer. $\newline$ $(4v - 1)^2 = 16v^2 - 8v + 1$ .