Find the product.
-$$( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$$
A) $49 p ^ { 3 } - 1$
B) $343 p ^ { 3 } + 56 p ^ { 2 } - 1$
C) $343 p ^ { 3 } + 1$
D) $343 p ^ { 3 } - 1$

Question

Quizplus · Accepted Answer

To find the product, distribute each term in the first polynomial across the second polynomial: $$(7p - 1)(49p^2 + 7p + 1) = 7p(49p^2) + 7p(7p) + 7p(1) - 1(49p^2) - 1(7p) - 1(1).$$ This simplifies to $343p^3 + 49p^2 + 7p - 49p^2 - 7p - 1$, which further simplifies to $343p^3 - 1$, matching option D.

Find the Product (7p−1)(49p2+7p+1)( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)(7p−1)(49p2+7p+1)

Find the Product $( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$