Factor out the greatest common factor. Then, check to see if the resulting expression is a perfect square trinomial.
2y, 2y+5, and 2y+5
Practice makes perfect
We can begin by factoring out the greatest common factor. Each term is divisible by 2y. Let's factor out 2y.
8y^3+40y^2+50y
⇕
2y (4y^2+20y+25)
Let's say that 2y is one of the dimensions. This means that the other two dimensions come from the remaining expression.
4y^2+20y+25
Next, we try to rewrite the first and last terms as perfect squares.
4y^2+20y+ 25
⇕
( 2y)^2+20y+ 5^2
Next, we can verify if the entire expression is a perfect square trinomial. Let's check if the middle term, 20y, is equal to twice the product of a=2y and b=5.
2 a b ⇒ 2( 2y)( 5) ⇒ 20y
This means that the expression is a perfect square trinomial. Since all three terms of the expression are positive, the expression is the perfect square of a and b.
( 2y)^2+20y+ 5^2
⇕
( 2y+ 5)^2
This means that the length of two sides are |2y+5|. The third side is equal to |2y|. We use the absolute value notation because sides cannot have a negative length.
