evaluate (2x-1/2x)²
Answers
Answer:
Step-by-step explanation:
Multiply the numbers
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2
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1
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2
(2x{\color{#c92786}{-1}} \cdot {\color{#c92786}{\frac{1}{2}}}x)^{2}
(2x−1⋅21x)2
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2
(2x{\color{#c92786}{-\frac{1}{2}}}x)^{2}
(2x−21x)2
2
Combine multiplied terms into a single fraction
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2
(2x-\frac{1}{2}x)^{2}
(2x−21x)2
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2
(2x+\frac{-x}{2})^{2}
(2x+2−x)2
3
Find common denominator
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2
(2x+\frac{-x}{2})^{2}
(2x+2−x)2
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2
(\frac{2 \cdot 2x}{2}+\frac{-x}{2})^{2}
(22⋅2x+2−x)2
4
Combine fractions with common denominator
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2
(\frac{2 \cdot 2x}{2}+\frac{-x}{2})^{2}
(22⋅2x+2−x)2
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2
(\frac{2 \cdot 2x-x}{2})^{2}
(22⋅2x−x)2
5
Multiply the numbers
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2
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2
(\frac{{\color{#c92786}{2}} \cdot {\color{#c92786}{2}}x-x}{2})^{2}
(22⋅2x−x)2
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4
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2
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2
(\frac{{\color{#c92786}{4}}x-x}{2})^{2}
(24x−x)2
6
Combine like terms
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4
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2
(\frac{{\color{#c92786}{4x}}{\color{#c92786}{-x}}}{2})^{2}
(24x−x)2
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3
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2
(\frac{{\color{#c92786}{3x}}}{2})^{2}
(23x)2
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Solution
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Answer:
(2x-1/2x)²= (2x)²+(1/2x)²-2×2x×1/2x
= 4x²+1/4x²-2