Special Products of Polynomials
Key Questions
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The general form for multiplying two binomials is:
(x+a)(x+b)=x^2+(a+b)x+ab Special products:
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the two numbers are equal, so it's a square:
(x+a)(x+a)=(x+a)^2=x^2+2ax+a^2 , or
(x-a)(x-a)=(x-a)^2=x^2-2ax+a^2
Example :(x+1)^2=x^2+2x+1
Or:51^2=(50+1)^2=50^2+2*50+1=2601 -
the two numbers are equal, and opposite sign:
(x+a)(x-a)=x^2-a^2
Example :(x+1)(x-1)=x^2-1
Or:51*49=(50+1)(50-1)=50^2-1=2499
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Answer:
A trinomial that when factored gives you the square of a binomial
Explanation:
Given: What is a perfect square binomial?
A perfect square binomial is a trinomial that when factored gives you the square of a binomial.
Ex.
(a+b)^2 = a^2 + 2ab + b^2 Ex.
(2a + 3b)^2 = 4a^2 + 12ab + 9b^2
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