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Question

Difficulty: EasyMultiplying Polynomials

What is the expanded form of the product (a−3)(a+7)(a - 3)(a + 7)?

  1. A
    a2−21a^2 - 21
  2. a2+4a−21a^2 + 4a - 21Answer
  3. C
    a2−4a−21a^2 - 4a - 21
  4. D
    a2−17aa^2 - 17a

Answer

a2+4a−21a^2 + 4a - 21
The expression is properly expanded by distributing each term in the first binomial to each term in the second binomial, resulting in a2+7a−3a−21a^2 + 7a - 3a - 21. Combining the like terms (7a−3a7a - 3a) yields the final simplified polynomial a2+4a−21a^2 + 4a - 21.

Step-by-Step Solution

1
Multiply the first terms in each binomial.
a×a=a2a \times a = a^2
To begin distributing the first term of the first binomial.
2
Multiply the outer terms.
a×7=7aa \times 7 = 7a
To complete the distribution of the first term.
3
Multiply the inner terms.
−3×a=−3a-3 \times a = -3a
To begin distributing the second term of the first binomial.
4
Multiply the last terms in each binomial.
−3×7=−21-3 \times 7 = -21
To complete the distribution of the second term.
5
Combine the like middle terms to simplify the expression.
7a+(−3a)=4a7a + (-3a) = 4a
To write the polynomial in its fully simplified standard form, resulting in a2+4a−21a^2 + 4a - 21.

Key Concept

Multiplying Binomials
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Topics

Multiplying Polynomials

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