Topics
2. Polynomials
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United States of AmericaUT
Math II

2.03 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 is divided by a vertical and horizontal line into four smaller rectangles, rectangles $A$A, $B$B, $C$C, and $D$D. The horizontal line divides the width of the rectangle into two width as labeled on the left side. The upper width is labeled $3$3 units. The lower width is labeled $y$y units. The vertical line divides the length of the rectangle into two lengths as labeled on the bottom side. The horizontal length to the left of the vertical line is labeled $y$y units. The horizontal length to the right of the vertical line is labeled $7$7 units. The top-left rectangle is labeled $B$B and has a light blue fill. The top-right rectangle is labeled $D$D and has a light purple fill. The bottom-left rectangle is labeled $A$A and has a light green fill. The bottom-right rectangle is labeled $C$C and has a light blue fill.
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
2 min

Distribute and simplify the following:

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

Easy
1 min

Distribute the following using binomial distribution:

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

Easy
1 min

Distribute and simplify the following:

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

Easy
1 min
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Outcomes

II.A.SSE.1

Interpret quadratic and exponential expressions that represent a quantity in terms of its context.

II.A.SSE.1.a

Interpret parts of an expression, such as terms, factors, and coefficients.

II.A.APR.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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