Solve the problem.
-$$( 3 x + 7 y ) ( 3 x - 3 y + 1 )$$
A) $9 x ^ { 2 } + 21 x y + 3 x - 21 y ^ { 2 } + 7 y$
B) $9 x ^ { 2 } + 12 x y + 12 y ^ { 2 }$
C) $9 x ^ { 2 } - 9 x y + 3 x - 21 y ^ { 2 }$
D) $9 x ^ { 2 } + 12 x y + 3 x - 21 y ^ { 2 } + 7 y$

Question

Quizplus · Accepted Answer

To solve the given expression $(3x + 7y)(3x - 3y + 1)$, we apply the distributive property (FOIL method for binomials):- First, multiply $3x$ by each term in the second binomial: $3x \cdot 3x = 9x^2$, $3x \cdot (-3y) = -9xy$, and $3x \cdot 1 = 3x$.- Then, multiply $7y$ by each term in the second binomial: $7y \cdot 3x = 21xy$, $7y \cdot (-3y) = -21y^2$, and $7y \cdot 1 = 7y$.Combine like terms:- $9x^2$ (no other $x^2$ terms),- $-9xy + 21xy = 12xy$ (combining $x$ and $y$ terms),- $3x$ (no other $x$ terms),- $-21y^2$ (no other $y^2$ terms),- $7y$ (no other $y$ terms).Thus, the correct expression is $9x^2 + 12xy + 3x - 21y^2 + 7y$, which matches choice D.

Solve the Problem (3x+7y)(3x−3y+1)( 3 x + 7 y ) ( 3 x - 3 y + 1 )(3x+7y)(3x−3y+1)

Solve the Problem $( 3 x + 7 y ) ( 3 x - 3 y + 1 )$