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3-70.

Use a generic rectangle to multiply the following expressions. Write each solution both as a sum and as a product.

1. $(2x+5)(x+6)$

• Draw a generic rectangle and label the length and width.

 $2x$ $+5$ $x$ $+6$
• Fill in the grid by multiplying the length and width of each box.

 $2x$ $+5$ $x$ $2x^2$ $5x$ $+6$ $12x$ $30$

$(2x+5)(x+6)=2x^2+17x+30$

Write an equation showing the product is the sum of the parts.
Area as a sum: $2x^2+12x+5x+30=2x^2+17x+30$
Area as a product: $(2x+5)(x+6)$

1. $(m−3)(3m+5)$

• See the help for part (a).

 $m$ $-3$ $3m$ $3m^2$ $-9m$ $+5$ $5m$ $-15$

Area as product: $(m−3)(3m+5)$
Area as sum: $3m^2−4m−15$

1. $(12x+1)(x^2−5)$

• See the help for part (a).

 $\color{red}{12x}$ $\color{red}{+1}$ $\color{red}{x^2}$ $\color{red}{12x^3}$ $\color{red}{x^2}$ $\color{red}{-5}$ $\color{red}{-60x}$ $\color{red}{-5}$
1. $(3−5y)(2+y)$

• See the help for part (a).