Math: Middle School: Grades 6, 7 and 8 Quiz - Pre-Algebra - Monomials and Polynomials: Multiplying (Answers)
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As you have previous learned, a monomial is one number that stands on its own and a polynomial is two or more monomial numbers that are linked together in an equation by an addition sign (+), subtraction sign (-) or a multiplication sign (x). For example: 3x2 ● 5x5. The “●” symbol will be used here in place of the normal “x” used for multiplication so as to not confuse “x” with “x” in algebra problems.
[readmore]When multiplying monomials, any exponents are added together. So in the example 3x2 ● 5x5, “2” and “5” will be added and the equations will then look like:
3x2 ● 5x5
3 ● 5 = 15x7
When multiplying polynomials, any exponents are added. Let’s look at the following example: (3x3)(4x4). [Note: This is a polynomial. When the “●” is replaced with parentheses(), the numbered problem becomes a polynomial and the parentheses indicate that we will be multiplying the two monomial numbers.] This problem is worked as follows to find the solution.
(3x3)(4x4)
3 ● 4 = 12
x3 + x4 = x7
Solution: 12x7
Now let’s look at the next example of 2x(3x + 7) and see how to find the solution.
2x(3x + 7)
(2x)(3x) + (2x)(7)
6x2 + 14x
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4x(5x2 - 2x + 3)
(4x)(5x2) = 20x3(add exponents) (4x)(-2x) = -8x2 (add exponents) (4x)(3) = 12x Solution: 20x3 - 8x2 + 12x Answer (a) is the correct solution |
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(8x5)(3x2)
8 ● 3 = 24 x5 + x2 = x7 Solution: 24x7 Answer (c) is the correct solution |
7x(4x2 + 3x + 12)
(7x)(4x2) = 28x3(add exponents) (7x)(3x) = 21x2(add exponents) (7x)(12) = 84x Solution: 28x3 + 21x2 + 84x Answer (d) is the correct solution |
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12x4 ● 10x2
12 ● 10 = 120x6 (remember to add exponents) Solution: 120x6 Answer (a) is the correct solution |
10x(5x2 - 9x + 22)
(10x)(5x2) = 50x3 (add exponents) (10x)(-9x) = -90x2 (add exponents) (10x)(22) = 220x Solution: 50x3 - 90x2 + 220x Answer (c) is the correct solution |
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(21x9)(8x3)
21 ● 8 = 168 x9 + x3 = x12 Solution: 168x12 Answer (b) is the correct solution |
3x(17x4 + 5x2 + 13)
(3x)(17x4) = 51x5 (add exponents) (3x)(5x2) = 15x3 (add exponents) (3x)(13) = 39x Solution: 51x5 + 15x3 + 39x Answer (d) is the correct solution |
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15x2 ● 5x8
15 ● 5 = 75x10 (remember to add exponents) Solution: 75x10 Answer (a) is the correct solution |
x(20x2 + 10x + 100)
(x)(20x2) = 20x3 (add exponents) (x)(10x) = 10x2 (add exponents) (x)(100) = 100x Solution: 20x3 + 10x2 + 100x Answer (c) is the correct solution |
6 ● 3 = 18x9 (remember to add exponents)
Solution: 18x9
Answer (b) is the correct solution