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3. Quadratic Equations, Functions & Polynomials
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Algebra 1

2.34 Multiplying polynomials

Lesson
Practice

Interactive practice questions

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.
a

What is the area of rectangle $A$A?

b

What is the area of rectangle $B$B?

c

What is the area of rectangle $C$C?

d

What is the area of rectangle $D$D?

e

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
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Outcomes

A.APR.A.1

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

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