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Chapter 0: Problem 41

Find each product. $$(x+2)^{2}$$

Short Answer

Expert verified
\((x+2)^{2}\) = \(x^{2} + 4x + 4\)

Step by step solution

01

Identify the components

In the expression \((x + 2)^2\), 'x' is 'a', '2' is 'b', and the exponent '2' is 'n'. So, our task is to apply the formula \((a+b)^2 = a^2 + 2ab + b^2\) to the expression.
02

Apply the binomial theorem

By applying the expansion, we can substitute 'a' with 'x' and 'b' with '2' to the formula. This gives us \(a^2 + 2ab + b^2\) = \(x^2 + 2 * x * 2 + 2^2\). This simplifies to \(x^2 + 4x + 4\).
03

Simplify the result

The final answer for the expanded form of \((x + 2)^2\) is \(x^2 + 4x + 4\). This is the expanded form of the given binomial equation.

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Most popular questions from this chapter

Simplify using properties of exponents. $$\left(x^{\frac{4}{5}}\right)^{5}$$

Simplify using properties of exponents. $$\left(3 x^{\frac{2}{3}}\right)\left(4 x^{\frac{3}{4}}\right)$$

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{-\frac{5}{4} y^{\frac{1}{3}}}}{x^{-\frac{3}{4}}}\right)^{-6} $$

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{\frac{1}{2}} y^{-\frac{7}{4}}}{y^{-\frac{5}{4}}}\right)^{-4} $$

a. Simplify: \(21 x+10 x\) b. Simplify: \(21 \sqrt{2}+10 \sqrt{2}\)
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