Question

1. $y(y + 4) - y(y - 3) - 9y$
2. $6x(2x - 3) - 5(2x^2 + 9x - 3)$
3. $2y(6x - 4x^2y) + 13x^2y^2 - 6$
4. $-2(3m^3 + 6) + 3m(2m^2 + 3m + 1)$
5. $3v(7v - 2) + 3(v^2 + 2v + 1) - 3v(-5v + 3)$
6. $4x^2(2x^2 + x - 5) - x(x^3 + 5x^2 - 3) + 17$
7. $-2r(r^3 - 6r^2 + 6) + 4r^3 - (5r^4 + 10r)$
8. $4b2a^2 - 5(3ab - 2b^2) + 29ab^2$
9. find the area of the trapezoid as a simplified expression.

$8x^2 + 3x$
$4x^2$
$2x^3 - x$

Explanation:

Let's solve problem 17: \( y(y + 4) - y(y - 3) - 9y \)

Step 1: Distribute the \( y \) terms

First, we distribute \( y \) in \( y(y + 4) \) and \( y \) in \( y(y - 3) \).
\( y(y + 4) = y^2 + 4y \)
\( y(y - 3) = y^2 - 3y \)
So the expression becomes: \( (y^2 + 4y) - (y^2 - 3y) - 9y \)

Step 2: Remove the parentheses

When we remove the parentheses, we have to distribute the negative sign in front of \( (y^2 - 3y) \):
\( y^2 + 4y - y^2 + 3y - 9y \)

Step 3: Combine like terms

Now we combine the \( y^2 \) terms, the \( y \) terms:

• For \( y^2 \) terms: \( y^2 - y^2 = 0 \)
• For \( y \) terms: \( 4y + 3y - 9y = (4 + 3 - 9)y = -2y \)

Answer:

\( -2y \)