Question

multiply binomials by polynomials: area model
a rectangle has a height of 2y^3 + 5 and a width of y^2 + 6y.
express the area of the entire rectangle.
your answer should be a polynomial in standard form.
area =

Explanation:

Step1: Multiply first - term of height by width

$(2y^{3})(y^{2}+6y)=2y^{3}\times y^{2}+2y^{3}\times6y = 2y^{5}+12y^{4}$

Step2: Multiply second - term of height by width

$5(y^{2}+6y)=5\times y^{2}+5\times6y = 5y^{2}+30y$

Step3: Combine like - terms

$(2y^{5}+12y^{4})+(5y^{2}+30y)=2y^{5}+12y^{4}+5y^{2}+30y$

Answer:

$2y^{5}+12y^{4}+5y^{2}+30y$