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 big 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 of the big rectangle, with length and width labeled to measure $y$y, indicating their unknown measure. Rectangle $B$B is situated above $A$A, at the top left side of the big rectangle, with width measuring $3$3 units. The bottom side of Rectangle $B$B is same as the top side of Rectangle $A$A. Rectangle $C$C is located at the bottom right of the big rectangle with length measuring $7$7 units. The left side of Rectangle $C$C is same as the right side of Rectangle $A$A. Rectangle $D$D is situated above $C$C, at the right of $B$B, at the top right side of the big rectangle. The bottom side of Rectangle $D$D is same as the top side of Rectangle $C$C. And the left side of Rectangle $D$D is same as the right side of Rectangle $B$B.
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

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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