Polynomial Multiplication Math Example 2

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Example 2

medium
Expand (2x−1)(x2+3x−5)(2x - 1)(x^2 + 3x - 5).

Solution

  1. 1
    Step 1: Distribute 2x2x: 2x⋅x2+2x⋅3x+2x⋅(−5)=2x3+6x2−10x2x \cdot x^2 + 2x \cdot 3x + 2x \cdot (-5) = 2x^3 + 6x^2 - 10x.
  2. 2
    Step 2: Distribute −1-1: −1⋅x2+(−1)⋅3x+(−1)⋅(−5)=−x2−3x+5-1 \cdot x^2 + (-1) \cdot 3x + (-1) \cdot (-5) = -x^2 - 3x + 5.
  3. 3
    Step 3: Combine: 2x3+6x2−x2−10x−3x+5=2x3+5x2−13x+52x^3 + 6x^2 - x^2 - 10x - 3x + 5 = 2x^3 + 5x^2 - 13x + 5.
  4. 4
    Check: At x=1x = 1: (1)(1+3−5)=−1(1)(1+3-5) = -1 and 2+5−13+5=−12+5-13+5 = -1 ✓

Answer

2x3+5x2−13x+52x^3 + 5x^2 - 13x + 5
When multiplying a binomial by a trinomial, distribute each term of the binomial to every term of the trinomial, then combine like terms. This generalizes FOIL beyond two binomials.

About Polynomial Multiplication

Multiplying polynomials by distributing every term in one polynomial to every term in the other, then combining like terms.

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More Polynomial Multiplication Examples

Example 1 easy

Multiply [formula] using FOIL.

Example 3 easy

Multiply [formula].

Example 4 hard

Expand [formula].

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