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Pre-Algebra - Monomials and Polynomials: Multiplying
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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.
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
(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
21 ● 8 = 168
x9 + x3 = x12
Solution: 168x12
Answer (b) is the correct solution
(4x)(5x2) = 20x3(add exponents)
(4x)(-2x) = -8x2 (add exponents)
(4x)(3) = 12x
Solution: 20x3 - 8x2 + 12x
Answer (a) is the correct solution
(10x)(5x2) = 50x3 (add exponents)
(10x)(-9x) = -90x2 (add exponents)
(10x)(22) = 220x
Solution: 50x3 - 90x2 + 220x
Answer (c) is the correct solution
12 ● 10 = 120x6 (remember to add exponents)
Solution: 120x6
Answer (a) is the correct solution
8 ● 3 = 24
x5 + x2 = x7
Solution: 24x7
Answer (c) is the correct solution
(3x)(17x4) = 51x5 (add exponents)
(3x)(5x2) = 15x3 (add exponents)
(3x)(13) = 39x
Solution: 51x5 + 15x3 + 39x
Answer (d) is the correct solution
15 ● 5 = 75x10 (remember to add exponents)
Solution: 75x10
Answer (a) is the correct solution
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(7x)(4x2) = 28x3(add exponents)
(7x)(3x) = 21x2(add exponents)
(7x)(12) = 84x
Solution: 28x3 + 21x2 + 84x
Answer (d) is the correct solution