Multiplying Polynomials
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In these lessons, we will learn how to multiply polynomials.
a) 5(x + y)
b) – 2x(y + 3)
c) 5x(x2 – 3)
d) –2x3(x2 – 3x + 4)
b) – 2x(y + 3) = – 2xy – 6x
c) 5x(x2 – 3) = 5x3– 15x
d) –2x3(x2 – 3x + 4) = –2x5 + 6x4 – 8x3
= x(2x + 5) + 1(2x + 5)
= 2x2 + 5x + 2x + 5
= 2x2 + 7x + 5
= 3y(5y2 – 2y + 3) – 4(5y2 – 2y + 3)
= 15y3 – 6y2 + 9y – 20y2 + 8y – 12
= 15y3 – 26y2 + 17y – 12
The first type is a trinomial that comes from squaring a binomial. (It is also called a perfect square)
Its general form is
(A + B)2 = A2 + 2AB + B2
(y – 3)2 = y2– 6y + 9
The second type is a binomial that comes from multiplying two binomials. (It is also called the difference of two squares)
Its general form is
(A + B)(A – B) = A2 – B2
(5y – 7)(5y + 7) = 25y2 - 49
Multiplying Monomials and/or Binomials and FOIL
We multiply monomials and binomials using different methods, including the distributive property and FOIL. FOIL is a mnemonic device to remember how to find the product of two binomials: we multiply the First, Outer, Inner, and then Last terms in each binomial. When multiplying monomials and binomials, it is important to remember the rules of multiplying exponents. How to multiply a binomial and a trinomial by distributing each of the terms in the binomial through the trinomial? Multiplying polynomials
Special products: Difference of Two Squares and Perfect Square. Multiplying Polynomials
This video explains how to multiply monomials and polynomials. Multiplying Polynomials - Slightly Harder Examples #1 Multiplying Polynomials - Slightly Harder Examples #2
Multiply a trinomial by a trinomial.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
More Lessons on Algebra
Free Math Worksheets
In these lessons, we will learn how to multiply polynomials.
Multiplying Polynomials and Monomials
When finding the product of a monomial and a polynomial, we multiply the monomial by each term of the polynomial. Be careful with the sign (+ or –) of each term.Example:
Evaluatea) 5(x + y)
b) – 2x(y + 3)
c) 5x(x2 – 3)
d) –2x3(x2 – 3x + 4)
Solution:
a) 5(x + y) = 5x + 5yb) – 2x(y + 3) = – 2xy – 6x
c) 5x(x2 – 3) = 5x3– 15x
d) –2x3(x2 – 3x + 4) = –2x5 + 6x4 – 8x3
Multiplying Polynomials and Polynomials
The multiplication of polynomials having more than one term requires the repeated use of the distributive property.Example
Multiply (2x + 5)(x +1)Solution:
(2x + 5)(x + 1)= x(2x + 5) + 1(2x + 5)
= 2x2 + 5x + 2x + 5
= 2x2 + 7x + 5
Example:
Multiply (5y2– 2y + 3)(3y – 4)Solution:
(5y2 – 2y + 3)(3y – 4)= 3y(5y2 – 2y + 3) – 4(5y2 – 2y + 3)
= 15y3 – 6y2 + 9y – 20y2 + 8y – 12
= 15y3 – 26y2 + 17y – 12
Multiplying Polynomials – Special Products
We will now consider two special types of products of binomials.The first type is a trinomial that comes from squaring a binomial. (It is also called a perfect square)
Its general form is
(A + B)2 = A2 + 2AB + B2
Example:
(x + 5)2 = x2 + 10x + 25(y – 3)2 = y2– 6y + 9
The second type is a binomial that comes from multiplying two binomials. (It is also called the difference of two squares)
Its general form is
(A + B)(A – B) = A2 – B2
Example:
(x + 4)(x – 4) = x2– 16(5y – 7)(5y + 7) = 25y2 - 49
We multiply monomials and binomials using different methods, including the distributive property and FOIL. FOIL is a mnemonic device to remember how to find the product of two binomials: we multiply the First, Outer, Inner, and then Last terms in each binomial. When multiplying monomials and binomials, it is important to remember the rules of multiplying exponents. How to multiply a binomial and a trinomial by distributing each of the terms in the binomial through the trinomial? Multiplying polynomials
Special products: Difference of Two Squares and Perfect Square. Multiplying Polynomials
This video explains how to multiply monomials and polynomials. Multiplying Polynomials - Slightly Harder Examples #1 Multiplying Polynomials - Slightly Harder Examples #2
Multiply a trinomial by a trinomial.
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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