Multiply the polynomials by using the distributive property. $$( m + 9 n ) \left( m ^ { 2 } + 8 m n - 2 n ^ { 2 } \right)$$
A) $m ^ { 3 } + 87 m ^ { 2 } n ^ { 2 } - 18 n ^ { 3 }$
B) $m ^ { 3 } + 17 m ^ { 2 } n + 70 m n ^ { 2 } - 18 n ^ { 3 }$
C) $m ^ { 3 } + 9 m n + 70 m n ^ { 2 } - 18 n ^ { 3 }$
D) $m ^ { 3 } + 9 n + 8 m n - 18 n ^ { 3 }$

Question

Quizplus · Accepted Answer

To multiply the polynomials, apply the distributive property (also known as the FOIL method for binomials). Multiply each term in the first polynomial by each term in the second polynomial and then combine like terms:1. $m \times m^2 = m^3$2. $m \times 8mn = 8m^2n$3. $m \times (-2n^2) = -2mn^2$4. $9n \times m^2 = 9m^2n$5. $9n \times 8mn = 72mn^2$6. $9n \times (-2n^2) = -18n^3$Combine like terms:- $m^3$ (no like terms to combine with)- $8m^2n + 9m^2n = 17m^2n$- $-2mn^2 + 72mn^2 = 70mn^2$- $-18n^3$ (no like terms to combine with)So, the result is $m^3 + 17m^2n + 70mn^2 - 18n^3$.

Multiply the Polynomials by Using the Distributive Property (m+9n)(m2+8mn−2n2)( m + 9 n ) \left( m ^ { 2 } + 8 m n - 2 n ^ { 2 } \right)(m+9n)(m2+8mn−2n2)

Multiply the Polynomials by Using the Distributive Property $( m + 9 n ) \left( m ^ { 2 } + 8 m n - 2 n ^ { 2 } \right)$