Multiplying Monomials With Polynomials
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2
3I. Model Problems
A monomial is an expression that is a number, variable or product of a
number and variables.
2
Examples of monomials: –3, 4x, 5xy, y
A polynomial is a monomial or the sum or difference of monomials.
4
3
2
Examples of polynomials: 2x + 4, –x
+ 4x
– 5x
, 400
To multiply monomials by a polynomial, multiply the monomial by
each of the terms of the polynomial.
2
2
Example Simplify 3x
(2x
+ 5x + 10).
2
2
2
2
= 3x
(2x
) + 3x
(5x) + 3x
(10)
Distributive property.
4
3
2
= 6x
+ 15x
+ 30x
Multiply.
4
3
2
The answer is 6x
+ 15x
+ 30x
.
II. Practice
Simplify.
2
2
1. 3(x
+ 2x + 6)
2. 5(x
+ 4x – 3)
2
2
3. 2(x
– x + 11)
4. 4(x
+ 2x + 30)
2
2
5. –3x(x
– 7x + 1)
6. –6x(3x
+ 5x – 10)
2
2
7. 5x(–2x
+ 8x + 12)
8. 8x(2x
+ 6x + 10)
2
2
2
2
9. 3x
(2x
+ 20x + 12)
10. 6x
(–2x
+ 5x – 30)
3
2
6
2
11. 9x
(x
+ x + 1)
(3x
– 12x + 30)
12. –5x
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