multiply the binomials using the foil method. combine like terms.

\(x^3 - 6)(5x^3 - 6)\

Question

multiply the binomials using the foil method. combine like terms.

\(x^3 - 6)(5x^3 - 6)\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "FOIL Method", "Product Rule of Exponents", "Polynomial Simplification" ], "new_concepts": [], "current_concepts": [ "FOIL Method", "Product Rule of Exponents", "Polynomial Simplification" ] } ## Apply the FOIL method Using the *FOIL Method* knowledge point $$ \begin{aligned} (x^3 - 6)(5x^3 - 6) &= \text{First} + \text{Outer} + \text{Inner} + \text{Last} \ &= (x^3)(5x^3) + (x^3)(-6) + (-6)(5x^3) + (-6)(-6) \end{aligned} $$ ## Multiply the individual terms Using the *Product Rule of Exponents* knowledge point $$ \begin{aligned} (x^3)(5x^3) &= 5x^{3+3} = 5x^6 \ (x^3)(-6) &= -6x^3 \ (-6)(5x^3) &= -30x^3 \ (-6)(-6) &= 36 \end{aligned} $$ ## Combine like terms Using the *Polynomial Simplification* knowledge point $$ \begin{aligned} 5x^6 - 6x^3 - 30x^3 + 36 &= 5x^6 + (-6 - 30)x^3 + 36 \ &= 5x^6 - 36x^3 + 36 \end{aligned} $$ Multiply the polynomials using the FOIL method. Combine like terms. $$(x^3 - 6)(5x^3 - 6) =$$ $5x^6 - 36x^3 + 36$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Multiplication" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Apply the FOIL method

Multiply the individual terms

Combine like terms

Answer: