Verify the Equality: (y+9)(2y-2) = 2y²-20y+18

Is equality correct?

$(y+9)(2y-2)=2y^2-20y+18$

To determine the correctness of the equation $(y+9)(2y-2)=2y^2-20y+18$, follow these steps:

• Step 1: Expand the left-hand side expression using the distributive property.

Start by applying the distributive property:
$(y + 9)(2y - 2) = y \cdot 2y + y \cdot (-2) + 9 \cdot 2y + 9 \cdot (-2)$

• Step 2: Calculate each term.

$y \cdot 2y = 2y^2$
$y \cdot (-2) = -2y$
$9 \cdot 2y = 18y$
$9 \cdot (-2) = -18$

• Step 3: Combine the terms.

Now, combine the terms:
$2y^2 - 2y + 18y - 18$

• Step 4: Simplify the expression.

This simplifies to:
$2y^2 + 16y - 18$

• Step 5: Compare with the right-hand side.

The expression $2y^2 + 16y - 18$ does not match the right-hand side $2y^2 - 20y + 18$.

Therefore, the original expression is not correct as given. The discrepancy appears to be in the linear terms. If we adjust one factor in the left-hand side, for example changing $y + 9$ to $y - 9$, we would get:

$(y - 9)(2y - 2) = 2y^2 - 20y + 18$, which would match the right side correctly.

Hence, the correct statement is: No, it must be $(y-9)$ instead of $(y+9)$.