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Question

Difficulty: EasyMultiplying Polynomials

Which of the following is equivalent to the expression (4p−1)(p+2)(4p - 1)(p + 2)?

  1. 4p2+7p−24p^2 + 7p - 2Answer
  2. B
    4p2−24p^2 - 2
  3. C
    4p2+9p−24p^2 + 9p - 2
  4. D
    11p−211p - 2

Answer

The equivalent expression is 4p2+7p−24p^2 + 7p - 2.
Using the distributive property (often remembered as FOIL), each term in the first binomial must be multiplied by each term in the second binomial. The products are 4p24p^2, 8p8p, −p-p, and −2-2. Combining the like terms (8p8p and −p-p) yields 7p7p, making the final simplified expression 4p2+7p−24p^2 + 7p - 2.

Step-by-Step Solution

1
Multiply the first terms of each binomial.
4p×p=4p24p \times p = 4p^2
This establishes the quadratic term of the final polynomial.
2
Multiply the outer terms.
4p×2=8p4p \times 2 = 8p
This finds the first part of the linear middle term.
3
Multiply the inner terms.
−1×p=−p-1 \times p = -p
This finds the second part of the linear middle term.
4
Multiply the last terms.
−1×2=−2-1 \times 2 = -2
This finds the constant term of the final polynomial.
5
Combine the like terms.
4p2+(8p−p)−2=4p2+7p−24p^2 + (8p - p) - 2 = 4p^2 + 7p - 2
Simplifying the expression converts it into standard polynomial form.

Key Concept

Multiplying Binomials
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Topics

Multiplying Polynomials

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