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Algebra 1
Section 10.2
Multiplying Polynomials
To multiply a monomial(1 term) and a trinomial(3 terms),
simply use the distributive property.
a(b + c + d)
= ab + ac + ad
1. 2x(x2 + 3x – 4)
= 2x(x2) + 2x(3x) + 2x(- 4)
= 2x3 + 6x2 – 8x
2. 4x2(5x3 – 2x2 + x)
= 4x2(5x3) + 4x2(-2x2) + 4x2(x)
= 20x5 – 8x4 + 4x3
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Multiply.
3. (3x – 7)(-2x)
4. (-x)(2x2 – 3x)
= -2x(3x) – 2x(-7) distributive property = -x(2x2) – x(-3x) dist. prop.
= -6x2 + 14x multiply
= -2x3 + 3x2 multiply
5. 3x2(5x – x3 + 2)
= 3x2(5x) + 3x2(-x3) + 3x2(2) distributive property
= 15x3 – 3x5 + 6x2 multiply
= -3x5 + 15x3 + 6x2 write in decreasing order of exponents
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To multiply 2 binomials(2 terms) use the FOIL method, which is
the distributive property in disguise.
Each letter of the word foil reminds you what terms to multiply.
First (terms in each set)
F
L
O uter (terms in each set)
(2x + 3)(3x + 2)
Inner (terms in each set)
I
L ast (terms in each set)
O
F
O
I
L
2x(3x) + 2x(2) + 3(3x) + 3(2)
= 6x2 + 4x + 9x + 6 (multiply terms)
= 6x2 + 13x + 6 (combine like terms)
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6. (3x – 2)(5x + 7)
F
O
I
L
3x(5x) + 3x(7) - 2(5x) - 2(7)
=
+ 21x – 10x – 14 multiply
= 15x2 + 11x – 14 combine like terms
15x2
8. (x – 5)(2x + 10)
I
F
O
L
x(2x) + x(10) - 5(2x) - 5(10)
7. (x – 4)(x + 4)
F
O
I
L
x(x) + x(4) - 4(x) - 4(4)
= x2 + 4x – 4x – 16 multiply
= x2 – 16 combine like terms
9. (-2x + 4)(-x – 3)
= -2x(-x) – 2x(-3) + 4(-x) + 4(-3)
= 2x2 + 6x – 4x – 12 multiply
= 2x2 + 2x – 12 combine like terms
= 2x2 + 10x – 10x – 50 multiply
= 2x2 – 50 combine like terms
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10. (5x + 4)(x2 – 3x + 2)
- use the distributive property, multiplying
each term in the first set, by each term in the
second set
= 5x(x2) + 5x(-3x) + 5x(2) + 4(x2) + 4(-3x) + 4(2)
= 5x3 – 15x2 + 10x + 4x2 – 12x + 8 multiply
= 5x3 – 11x2 – 2x + 8 combine like terms
11. (x2 + 9)(x2 – x – 4)
= x2(x2) + x2(-x) + x2(- 4) + 9(x2) + 9(-x) + 9(- 4)
= x4 – x3 – 4x2 + 9x2 – 9x – 36 multiply
= x4 – x3 + 5x2 – 9x – 36 combine like terms
distributive property
distributive property
© Mr. Sims
Multiply.
1.) 3x2(5x – x3 + 2)
2.) 2x(3x2 – 4x + 1)
3.) -x2(6x3 – 14x + 9)
4.) (3x + 5)(2x + 1)
5.) (2x – 3)(x + 3)
6.) (3x – 5)(2x + 1)
7.) (x + 2)(x + 6)
8.) (3x + 1)(2x + 2)
9.) (2x + 1)(x + 3)
10.) (2x + 1)(3x + 1)
11.) (2x2 – 7x + 1)(4x + 3)
12.) (x + 3)(x2 – 6x + 2)
13.) (2x – 1)(x + 9)
14.) (3x  4)  1 x  1
3
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Algebra 1
Section 10.2
Assignment
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15.)  x  1   x  5 
4 
4
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