factor the trinomial.

\5x^3y + 27x^2y^2 + 28xy^3 = \

Question

factor the trinomial.

\5x^3y + 27x^2y^2 + 28xy^3 = \

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor", "Factoring Polynomials" ], "new_concepts": [], "current_concepts": [ "Greatest Common Factor", "Factoring Polynomials", "Factoring Trinomials" ] } ## Factor out the greatest common factor $$ 5x^3y + 27x^2y^2 + 28xy^3 = xy(5x^2 + 27xy + 28y^2) $$ ## Factor the remaining quadratic trinomial $$ \begin{aligned} &5 \times 28 = 140\ &20 \times 7 = 140,\quad 20 + 7 = 27\ &5x^2 + 27xy + 28y^2 = 5x^2 + 20xy + 7xy + 28y^2\ &= 5x(x + 4y) + 7y(x + 4y)\ &= (5x + 7y)(x + 4y) \end{aligned} $$ ## Combine all factored parts $$ 5x^3y + 27x^2y^2 + 28xy^3 = xy(5x + 7y)(x + 4y) $$ Factor the trinomial. $5x^3y + 27x^2y^2 + 28xy^3 =$ $xy(5x + 7y)(x + 4y)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Factor the remaining quadratic trinomial

Combine all factored parts

Answer: