10.2 – multiplying polynomials i got polynomials…. they’re multiplying! and i’m losing a...
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10.2 – Multiplying Polynomials
I got polynomials….
They’re multiplying! And
I’m losing a binomial. Cause the power you’re
supplyin’, it’s terrifyin’.
Oh, you better distribute. Cause I need
an answer. And my calculator just won’t do.
Yeah, you better distribute, you better
understand, to my math, I must be true.
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Warm-Up
Simplify the following expressions.1. (x + 4)22. -3(2 – 5x)3. 7(12 + 3x) – 104. (3x)(-4x)5. 3x + (-4x)
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Homework Answers
20) -4; quadratic, trinomial
22) 5; quadratic, trinomial
24) 14; quartic, binomial
26) 7.4; cubic, binomial
28) 9; cubic, polynomial
30) -95; quartic, polynomial
32)
34)
36)
38)
a4 3a3 3a2 a
5y2 7
3x2 6x
7x4 x3 7x2 5x 9
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Journal Entry
• Is the following statement true?
• Answer this question in journal form in your notebook.– Think about ways that you could check it.– Make a decision: Yes or no?• Defend your answer with 2-3 sentences.• Tweet about it later: #mathswagg
2( 4)( 5) 20 x x x
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Discovery Activity
• Find the area of the large rectangle below!
5x cm 8 cm
2x cm
3 cm
***REMEMBER: AREA = LENGTH X WIDTH***
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Solution(5x + 8)(2x + 3) = 5x·2x + 5x·3 + 8·2x + 8·3
= 10x2 + 15x + 16x + 24= 10x2 + 31x + 24
5x cm 8 cm
2x cm
3 cm
10x2 16x
15x 24
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Multiplying Polynomials Using The Distributive Property
• Remember doing something like: 3(x - 5)?– This became: 3(x) + 3(-5)
• Which simplified to 3x - 15
• Now we are dealing with situations where we must do it twice!– Example: (4x – 9)(2x + 7)
• We simplify need to distribute all of the numbers in the first grouping to each of the numbers in the second grouping
Not just one number in front!
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General Rule
(a + b)(c + d)
a(c + d) + b(c + d)
ac + ad + bc + bd
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Example 1: iDo
(3a + 4)(2a + 1)Find the product.
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Example 2: iDo
(x + 4)(x - 5)Find the product.
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Example 3: WiiDo
(c - 3)(2c - 5)Find the product.
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Example 4: WiiDo
(2w + 3)(2w - 3)Find the product.
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Example 5: YouDo
(y + 5)(y + 7)Find the product.
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Example 6: YouDo
(3x - 5)(5x + 2)Find the product.
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So what if there’s a trinomial?
(a + b)(c + d + e) a(c + d + e) + b(c + d + e)ac + ad + ae + bc + bd + be
(a + b + c)(d + e) a(d + e) + b(d + e) + c(d + e)ad + ae + bd + be + cd + ce
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Last Example
(t2 + 6t – 8)(t – 6)Find the product.
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Boss/Secretary Practice• Students will work in pairs.• Materials: One worksheet, one calculator, one pencil per
pair• Students will be given one of two roles (you will
alternate these roles):– Boss: Tells the secretary how to solve the problem, is
the only one talking in the pair, does not write anything
– Secretary: Listens to the boss, writes everything, cannot talk unless (s)he is helping the boss
• Complete the worksheet in next before the end of class!
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Homework
pg. 587 #18-46 every other even(#18, 22, 26, 30, 34, 38, 42, 46)