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What is another way to write the expression 2(x+1)(x+2) ?
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Answered by
GPT-4o mini
To rewrite the expression \( 2(x+1)(x+2) \), we can start by expanding the product \( (x+1)(x+2) \).
1. Use the distributive property (also known as the FOIL method for binomials):
\[
(x + 1)(x + 2) = x \cdot x + x \cdot 2 + 1 \cdot x + 1 \cdot 2 = x^2 + 2x + x + 2 = x^2 + 3x + 2.
\]
2. Next, multiply the result by 2:
\[
2(x^2 + 3x + 2) = 2x^2 + 6x + 4.
\]
Therefore, another way to write the expression \( 2(x+1)(x+2) \) is:
\[
2x^2 + 6x + 4.
\]
1. Use the distributive property (also known as the FOIL method for binomials):
\[
(x + 1)(x + 2) = x \cdot x + x \cdot 2 + 1 \cdot x + 1 \cdot 2 = x^2 + 2x + x + 2 = x^2 + 3x + 2.
\]
2. Next, multiply the result by 2:
\[
2(x^2 + 3x + 2) = 2x^2 + 6x + 4.
\]
Therefore, another way to write the expression \( 2(x+1)(x+2) \) is:
\[
2x^2 + 6x + 4.
\]
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