Multiplying (2x + 3)(x² - x + 4)

Algebra 1 · Axiom Academy

EXAMPLE Multiplying Polynomials Multiply (2x + 3)(x^2 - x + 4) by complete distribution, using color to track every product. Multiply the binomial by the trinomial: (2x + 3)(x^2 - x + 4) . Distribute every term of the first factor across every term of the second, then combine like terms. Nice work — you multiplied a binomial by a trinomial by complete distribution. Remember: Distribute systematically: every term of the first polynomial multiplies every term of the second. Track with color: color-coding which term you are distributing keeps you from missing or doubling a product. Mind the exponents and signs: coefficients multiply, exponents add, and a negative term stays negative. Combine like terms: only terms with the same variable and exponent combine — here -2x^2 + 3x^2 = x^2 and 8x - 3x = 5x . Count your products: a (binomial)(trinomial) gives products before combining. Final answer: (2x + 3)(x^2 - x + 4) = 2x^3 + x^2 + 5x + 12 . The same systematic approach multiplies any two polynomials.

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