CPM Homework Help : AC Problem 9-40

Multiple Choice: Which of the following expressions is the product of $\left(4y-3x\right)\left(2y+x\right)$ ?

$8y^2-2xy-3x^2$

$6y^2-2xy-2x^2$

$8y^2+10xy-3x^2$

$6y^2-2x$

Hint 1:

Use a generic rectangle to multiply the expression together. Draw a rectangle and divide it into four equal parts.

Hint 2:

Multiply each row by each column. Add the products together to get the final product. Added to the rectangle: Exterior left edge top is negative 3, X. Exterior left edge bottom is 4, y. Exterior bottom edge left is 2, y. Exterior bottom edge right is x.

Answer:

$(4y−3x)(2y+x)=8y^2−2xy−3x^2$ Added to the rectangle: Interior upper left box is negative 6, x, y. Interior upper right box is negative 3, X squared. Interior lower left box is negative 8, y squared. Interior lower right box is 4, X, Y.