The area of the figure below is $\left(y+3\right)\left(y+7\right)$(y+3)(y+7). We want to find another expression for this area by finding the sum of the areas of the four smaller rectangles.

A rectangle segmented into four smaller rectangles: Rectangle $A$`A`, $B$`B`, $C$`C`, and $D$`D`. Rectangle $A$`A` is located at the bottom left with sides of length $y$`y`. Rectangle $B$`B`, situated above $A$`A`, has a length of $y$`y` and a width of $3$3. To the right of $A$`A`, Rectangle $C$`C` has a length of $7$7 and a width of $y$`y`. Rectangle $D$`D`, positioned above $C$`C`, has dimensions of $7$7 by $3$3. This layout represents the algebraic expression $\left(y+7\right)\left(y+3\right)$(`y`+7)(`y`+3), with the rectangle's length being $y+7$`y`+7 and its width $y+3$`y`+3.

What is the area of rectangle $A$A?

What is the area of rectangle $B$B?

What is the area of rectangle $C$C?

What is the area of rectangle $D$D?

Using the areas of each rectangle, write an equivalent expression for the area of the figure.

Easy

2min

Distribute and simplify the following:

$\left(x+2\right)\left(x+5\right)$(x+2)(x+5)

Easy

1min

Distribute the following using binomial distribution:

$\left(x+5\right)\left(x+7\right)$(x+5)(x+7)

Easy

1min

Distribute and simplify the following:

$\left(v+8\right)\left(v+10\right)$(v+8)(v+10)

Easy

1min

Outcomes

A1.10.B

Multiply polynomials of degree one and degree two

A1.10.D

Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property

7.03 Multiplying polynomials

Interactive practice questions

Outcomes

A1.10.B

A1.10.D

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