Multiplication of Monomials by Polynomials
Key Questions
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It works the same as with numbers. For numbers, you know that
#a(b+c)# equals#ab+ac# .
For the same reason, if you have a monomial and you want to multiplicate it by a polynomial (which is a sum of monomials with some coefficients!), you follow the same rule.For example, if your monomial is
#3x^2# , and your polynomial is#3+2x-5x^2+8x^3# , the product is
#3x^2(3+2x-5x^2+8x^3)#
you will calculate is as
#3x^2\cdot 3+3x^2\cdot2x-3x^2\cdot5x^2+3x^2\cdot8x^3# , which is
#9x^2 + 6x^3 - 15x^4 + 24x^5# -
Answer:
#=> a_1x^(p_1) * a_2x^(p_2)=a_1a_2x^(p_1+p_2)# Explanation:
A monomial is of the form:
#=> ax^p# where
#a# is a constant coefficient and#p# is a constant power.In the case of multiplying two monomials together:
#=>Ax^P equiv a_1x^(p_1) * a_2x^(p_2)# The coefficients will multiply, so:
#=> A =a_1 * a_2# The powers will sum, so:
#=> P =p_1 + p_2# Hence:
#=> Ax^P equiv a_1x^(p_1) * a_2x^(p_2)=a_1a_2x^(p_1+p_2)# For example:
#=>3x^2*2x# #=> (3*2)x^(2+1)# #=> 6x^3# -
Just distribute the monomial to each of the polynomial's terms
For example:
#(3m)(m^2 -2m + 1)# #=> (3m)(m^2) - (3m)(2m) + (3m)(1)#
#=> 3m^3 - 6m^2 + 3m#
Questions
Polynomials and Factoring
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Polynomials in Standard Form
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Addition and Subtraction of Polynomials
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Multiplication of Monomials by Polynomials
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Multiplication of Polynomials by Binomials
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Special Products of Polynomials
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Monomial Factors of Polynomials
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Zero Product Principle
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Factorization of Quadratic Expressions
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Factor Polynomials Using Special Products
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Factoring by Grouping
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Factoring Completely
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Probability of Compound Events