How do you simplify (a^3+2a^2b-ab^2+3b^3)(4ab)? Algebra Polynomials and Factoring Multiplication of Monomials by Polynomials 1 Answer Don't Memorise Aug 21, 2015 =color(blue)(4a^4b + 4a^3b^2 +12ab^4 Explanation: (a^3+2a^2b−ab^2+3b^3)color(blue)((4ab) =(a^3) * color(blue)((4ab)) +(2a^2b) * color(blue)((4ab)) - (ab^2) *color(blue)((4ab)) +(3b^3) .color(blue)((4ab) =4a^3*ab + 8a^2b*ab - 4ab^2*ab +12b^3*ab By property color(blue)(a^m*a^n=a^(m+n) Applying the same to powers of a and b =4a^((3+1))b + 8a^((2+1))b^((1+1)) - 4a^((1+1))b^((2+1)) +12ab^(3+1) =4a^4b + color(blue)(8a^3b^2 - 4a^2b^3) +12ab^4 =color(blue)(4a^4b + 4a^3b^2 +12ab^4 Answer link Related questions What is Multiplication of Monomials by Polynomials? How do you multiply monomials by polynomials? How do you multiply monomials by monomials? How do you multiply (3xy^5)(-6x^4y^2)? How do you multiply and simplify 6ab(-10a^2 b^3+c^5)? How do you simplify -3a^2b(9a^2-4b^2)? How do you multiply y(xy^4)? How do you multiply (2x-1)(x^3-2x^2+3x-4)? How do you multiply (5n^2)(2n^5 - 2n^3 3n^7)? How do you simplify 2t^2+(3+5)(4t)? See all questions in Multiplication of Monomials by Polynomials Impact of this question 2418 views around the world You can reuse this answer Creative Commons License