Find the product.
-$$[ ( 5 x + 1 ) + 3 y ] ^ { 2 }$$
A) $25 x ^ { 2 } + 30 x y + 9 y ^ { 2 }$
B) $25 x ^ { 2 } + 10 x + 1 + 30 x y + 6 y + 9 y ^ { 2 }$
C) $25 x ^ { 2 } + 5 x + 1 + 15 x y + 3 y + 9 y ^ { 2 }$
D) $25 x ^ { 2 } + 10 x + 30 x y + 6 y + 9 y ^ { 2 }$

Question

Quizplus · Accepted Answer

To find the product, we use the formula for the square of a binomial, $(a + b)^2 = a^2 + 2ab + b^2$, where $a = 5x + 1$ and $b = 3y$. Squaring $5x + 1$ gives $25x^2 + 10x + 1$, and squaring $3y$ gives $9y^2$. The cross term $2ab$ results in $2(5x + 1)(3y) = 30xy + 6y$. Adding these results together gives $25x^2 + 10x + 1 + 30xy + 6y + 9y^2$.

Find the Product [(5x+1)+3y]2[ ( 5 x + 1 ) + 3 y ] ^ { 2 }[(5x+1)+3y]2

Find the Product $[ ( 5 x + 1 ) + 3 y ] ^ { 2 }$