Expand. If necessary, combine like terms. (4x+1)(4x+1)=

Identify binomial: Identify the binomial to be squared. The binomial given is (4x+1), and we need to square it, which means we will multiply (4x+1) by itself.Write squared binomial: Write the binomial squared as a multiplication of two binomials. (4x+1)(4x+1) means that we are multiplying the binomial (4x+1) by itself.Use FOIL method: Use the FOIL method to expand the product of the two binomials. FOIL stands for First, Outer, Inner, Last, which refers to the terms in each binomial that are multiplied together. First: 4x * 4x = 16x^2 Outer: 4x * 1 = 4x Inner: 1 * 4x = 4x Last: 1 * 1 = 1Combine like terms: Combine like terms from the FOIL method. We have two like terms, 4x and 4x, from the outer and inner steps. 16x^2 + 4x + 4x + 1 16x^2 + (4x + 4x) + 1 16x^2 + 8x + 1Write final form: Write the final expanded form of the binomial squared. The final expanded form of (4x+1)(4x+1) is 16x^2 + 8x + 1.

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Math Problems

Algebra 1

Multiply two binomials: special cases

Full solution

Q. Expand. If necessary, combine like terms.

\newline

(4x+1)(4x+1)=

Identify binomial: Identify the binomial to be squared. $\newline$ The binomial given is $(4x+1)$ , and we need to square it, which means we will multiply $(4x+1)$ by itself.
Write squared binomial: Write the binomial squared as a multiplication of two binomials. $\newline$ $(4x+1)(4x+1)$ means that we are multiplying the binomial $(4x+1)$ by itself.
Use FOIL method: Use the FOIL method to expand the product of the two binomials. $\newline$ FOIL stands for First, Outer, Inner, Last, which refers to the terms in each binomial that are multiplied together. $\newline$ First: $4x \times 4x = 16x^2$ $\newline$ Outer: $4x \times 1 = 4x$ $\newline$ Inner: $1 \times 4x = 4x$ $\newline$ Last: $1 \times 1 = 1$
Combine like terms: Combine like terms from the FOIL method. $\newline$ We have two like terms, $4x$ and $4x$ , from the outer and inner steps. $\newline$ $16x^2 + 4x + 4x + 1$ $\newline$ $16x^2 + (4x + 4x) + 1$ $\newline$ $16x^2 + 8x + 1$
Write final form: Write the final expanded form of the binomial squared. $\newline$ The final expanded form of $(4x+1)(4x+1)$ is $16x^2 + 8x + 1$ .