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Difficulty: EasyEquivalent Algebraic Expressions

Which of the following expressions is equivalent to 3(x2−2x)−2(x2−5x)3(x^2 - 2x) - 2(x^2 - 5x) for all values of xx?

  1. A
    x2−16xx^2 - 16x
  2. x2+4xx^2 + 4xAnswer
  3. C
    x2−4xx^2 - 4x
  4. D
    5x2−16x5x^2 - 16x

Answer

x2+4xx^2 + 4x
To simplify the given expression, distribute the coefficients outside the parentheses to each term inside. Distributing 33 to (x2−2x)(x^2 - 2x) yields 3x2−6x3x^2 - 6x. Distributing −2-2 to (x2−5x)(x^2 - 5x) yields −2x2+10x-2x^2 + 10x. Grouping and combining the like terms gives (3x2−2x2)+(−6x+10x)(3x^2 - 2x^2) + (-6x + 10x), which simplifies to x2+4xx^2 + 4x.

Step-by-Step Solution

1
Distribute the number 33 to the terms in the first set of parentheses.
3(x2−2x)=3x2−6x3(x^2 - 2x) = 3x^2 - 6x
To eliminate the parentheses by multiplying each term inside by the outer coefficient.
2
Distribute the number −2-2 to the terms in the second set of parentheses.
−2(x2−5x)=−2x2+10x-2(x^2 - 5x) = -2x^2 + 10x
To eliminate the second set of parentheses, remembering that multiplying two negative numbers yields a positive product: −2×−5x=10x-2 \times -5x = 10x.
3
Combine like terms by grouping the quadratic terms and the linear terms together.
(3x2−2x2)+(−6x+10x)=x2+4x(3x^2 - 2x^2) + (-6x + 10x) = x^2 + 4x
To simplify the expression by adding or subtracting the coefficients of terms with the same variable power.

Key Concept

Equivalent Algebraic Expressions
Estimated Time:45s
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Topics

Equivalent Algebraic Expressions

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