Topic 7.2 & 7.3 - Multiplying Polynomials LESSON

Math Response

Let's do a basic distributive problem:

$$-3\left(5x+7\right)$$

Type answer here

Correct Answer: -15x-21

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Math Response

What would you get if you changed the multiplier to this?

$$-3x\left(5x+7\right)$$

Type answer here

Correct Answer: -15x^2-21x

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​Remember when multiplying exponents with the same bases you ADD the powers together!

So -3x (5x) would be -15x²

Math Response

Ok, so try multiplying a binomial with another binomial. You will probably be wrong...that is ok! :)

$$\left(2x+4\right)\left(3x-5\right)$$

Type answer here

Correct Answer: 6x^2+2x-20

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Math Response

Ok, now try this one.

$$\left(5x-4\right)\left(2x+1\right)$$

Type answer here

Correct Answer: 10x^2-3x-4

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Math Response

Now, let's try a TRINOMIAL times a binomial! It isn't really much different...so you should be ok!

$$\left(x^2+2x-1\right)\left(3x+4\right)$$

Type answer here

Correct Answer: 3x^3+10x^2+5x-4

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​Topic 7.3 - Special Cases of Binomials

There are 3 scenarios when multiplying binomials that have a specific outcome. These cases can quickly be solved if you remember the outcome...but you do NOT have to in order to solve them!

That said, when FACTORING POLYNOMIALS, it is very helpful to know these shortcuts!

​​Do you notice anything about both answers when compared to the given problem?

This pattern will ALWAYS work!

​(This should be +16!)

Match

Match each problem with the special pattern it creates.

• $$\left(a+b\right)^2$$

• $$\left(a-b\right)^2$$

• $$\left(a+b\right)\left(a-b\right)$$

a² + 2ab + b²

a² - 2ab + b²

a² - b²

• a² + 2ab + b²

• a² - 2ab + b²

• a² - b²

Math Response

What polynomial represents the area of the smartphone's screen?

Type answer here

Correct Answer: 1.8x^2+4.8x+3

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Math Response

John is placing cement tiles for a patio in a rectangle surrounding a rectangular fire pit. The fire pit has a width of x ft and a length that is 5 times the width. The entire patio is 7 ft wider and 17 ft longer than the fire pit. What is the area that he will need to buy tiles for?

Type answer here

Correct Answer: 52x+11

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Math Response

What is the polynomial expression that represents how much land the second child gets.

(use x instead of z)

Type answer here

Correct Answer: 4x+4

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