Multiply the polynomials by using the distributive property.
-$( n - 6 p ) \left( n ^ { 2 } - 5 n p + 3 p ^ { 2 } \right)$
A) $n ^ { 3 } - 6 p - 5 n p - 18 p ^ { 3 }$
B) $n ^ { 3 } - 6 n p + 33 n p ^ { 2 } - 18 p ^ { 3 }$
C) $n ^ { 3 } + 22 n ^ { 2 } p ^ { 2 } - 18 p ^ { 3 }$
D) $n ^ { 3 } - 11 n ^ { 2 } p + 33 n p ^ { 2 } - 18 p ^ { 3 }$

Question

Quizplus · Accepted Answer

To multiply the polynomials using the distributive property, each term in the first polynomial $(n - 6p)$ is multiplied by each term in the second polynomial $(n^2 - 5np + 3p^2)$, and then the results are added together. This gives:- $n \times n^2 = n^3$- $n \times (-5np) = -5n^2p$- $n \times 3p^2 = 3np^2$- $(-6p) \times n^2 = -6np^2$- $(-6p) \times (-5np) = 30np^2$- $(-6p) \times 3p^2 = -18p^3$Adding these results together:$n^3 - 5n^2p + 3np^2 - 6np^2 + 30np^2 - 18p^3 = n^3 - 5n^2p + (3 - 6 + 30)np^2 - 18p^3 = n^3 - 5n^2p + 27np^2 - 18p^3$This simplifies to:$n^3 - 11n^2p + 33np^2 - 18p^3$Therefore, the correct answer is D.

Multiply the Polynomials by Using the Distributive Property (n−6p)(n2−5np+3p2)( n - 6 p ) \left( n ^ { 2 } - 5 n p + 3 p ^ { 2 } \right)(n−6p)(n2−5np+3p2)

Multiply the Polynomials by Using the Distributive Property $( n - 6 p ) \left( n ^ { 2 } - 5 n p + 3 p ^ { 2 } \right)$