Section 7.3: Multiplying Polynomials
To multiply polynomials, use the distributive property to multiply each term in the first polynomial by each term in the second polynomial, then combine like terms.
Example 1
Multiply: \( (x + 3)(x + 5) \)
Distribute each term:
\( x \cdot x + x \cdot 5 + 3 \cdot x + 3 \cdot 5 = x^2 + 5x + 3x + 15 = x^2 + 8x + 15 \)
Example 2
Multiply: \( (2x - 1)(x^2 + x + 4) \)
Distribute \( 2x \) and \(-1\) across the second polynomial:
\( 2x(x^2 + x + 4) - 1(x^2 + x + 4) = 2x^3 + 2x^2 + 8x - x^2 - x - 4 = 2x^3 + x^2 + 7x - 4 \)
Practice Problems
- \( (x + 2)(x + 7) \)
- \( (3y - 4)(y + 5) \)
- \( (x + 1)(x^2 + x + 1) \)
- \( (2a - 3)(a^2 + 2a - 5) \)
- \( (x - 4)(x + 4) \)