Question

4 - 6. multiply the expressions below using an area model. homework help

4 - 7. write the area of the rectangle below as a sum and as a product. homework help

Explanation:

Step1: Find the sum

Add all the terms in the rectangle:

$$\begin{align*} &-x-3y + 5+2x^{2}+6xy-10x\\ =&2x^{2}+6xy+(-x-10x)-3y + 5\\ =&2x^{2}+6xy-11x-3y + 5 \end{align*}$$

Step2: Find the product

Factor the terms. First, find the greatest common factor of the terms in each row and column.
For the first row: terms are \(-x,-3y,5\)
For the second row: terms are \(2x^{2},6xy,-10x\)
The length of the rectangle: \(2x - y - 5\) (by factoring out common factors from columns)
The width of the rectangle: \(x+ 3y-2\) (by factoring out common factors from rows)
The product is \((2x - y - 5)(x + 3y-2)\)

Answer:

Sum: \(2x^{2}+6xy-11x-3y + 5\)
Product: \((2x - y - 5)(x + 3y-2)\)