Expand. If necessary, combine like terms. (2x+3)^(2)=

Recognize the pattern: Recognize the pattern. The expression (2x+3)^(2) is in the form of (a+b)^2, which is a special case of binomial expansion. Special case: (a + b)^2 = a^2 + 2ab + b^2Identify values of a and b: Identify the values of a and b. In the expression (2x+3)^(2), compare it with (a+b)^2 to find: a = 2x b = 3Apply binomial square formula: Apply the binomial square formula. Using the formula (a + b)^2 = a^2 + 2ab + b^2, we substitute a and b with 2x and 3, respectively: (2x + 3)^2 = (2x)^2 + 2*(2x)*(3) + (3)^2Perform the calculations: Perform the calculations. Now we calculate each term: (2x)^2 = 4x^2 2*(2x)*(3) = 12x (3)^2 = 9Combine the calculated terms: Combine the calculated terms. Combine the terms to get the expanded form: (2x + 3)^2 = 4x^2 + 12x + 9

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Math Problems

Algebra 1

Multiply two binomials: special cases

Full solution

Q. Expand. If necessary, combine like terms.

\newline

(2x+3)^{2}=

Recognize the pattern: Recognize the pattern. $\newline$ The expression $(2x+3)^{2}$ is in the form of $(a+b)^2$ , which is a special case of binomial expansion. $\newline$ Special case: $(a + b)^2 = a^2 + 2ab + b^2$
Identify values of a and b: Identify the values of a and b. $\newline$ In the expression $(2x+3)^{2}$ , compare it with $(a+b)^2$ to find: $\newline$ a = $2$ x $\newline$ b = $3$
Apply binomial square formula: Apply the binomial square formula. $\newline$ Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we substitute $a$ and $b$ with $2x$ and $3$ , respectively: $\newline$ $(2x + 3)^2 = (2x)^2 + 2\cdot(2x)\cdot(3) + (3)^2$
Perform the calculations: Perform the calculations. $\newline$ Now we calculate each term: $\newline$ $(2x)^2 = 4x^2$ $\newline$ $2 \cdot (2x) \cdot (3) = 12x$ $\newline$ $(3)^2 = 9$
Combine the calculated terms: Combine the calculated terms. $\newline$ Combine the terms to get the expanded form: $\newline$ $(2x + 3)^2 = 4x^2 + 12x + 9$