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What can a perfect square trinomial can be factored as?
It can be factored as the SQUARE OF A BINOMIAL
How do you factor the perfect square binomial?
(a^2 - b^2) = (a - b)(a + b)
What is similar about a perfect square trinomial and a difference of two squares?
Each has two binomial factors.
What special product results to a perfect square trinomial?
A perfect square trinomial results from squaring a binomial. Specifically, when a binomial of the form ( (a + b) ) or ( (a - b) ) is squared, it expands to ( a^2 + 2ab + b^2 ) or ( a^2 - 2ab + b^2 ), respectively. Both forms yield a trinomial where the first and last terms are perfect squares, and the middle term is twice the product of the binomial’s terms.
Is the square of a binomial ever a binomial?
no
What can a perfect square trinomial can be factored as?
It can be factored as the SQUARE OF A BINOMIAL
How do you factor the perfect square binomial?
(a^2 - b^2) = (a - b)(a + b)
How do you complete the square to make a binomial a perfect-square trinomial?
The binomial usually has an x2 term and an x term, so we complete the square by adding a constant term. If the coefficient of x2 is not 1, we divide the binomial by that coefficient first (we can multiply the trinomial by it later). Then we divide the coefficient of x by 2 and square that. That is the constant that we need to add to get the perfect square trinomial. Then just multiply that trinomial by the original coefficient of x2.
What is similar about a perfect square trinomial and a difference of two squares?
Each has two binomial factors.
What must be added to the binomial m2-12m to make it a perfect square trinomial?
-10
What special product results to a perfect square trinomial?
A perfect square trinomial results from squaring a binomial. Specifically, when a binomial of the form ( (a + b) ) or ( (a - b) ) is squared, it expands to ( a^2 + 2ab + b^2 ) or ( a^2 - 2ab + b^2 ), respectively. Both forms yield a trinomial where the first and last terms are perfect squares, and the middle term is twice the product of the binomial’s terms.
Is the square of a binomial ever a binomial?
no
How do you factor perfect square binomial?
Remember to factor out the GCF of the coefficients if there is one. A perfect square binomial will always follow the pattern a squared plus or minus 2ab plus b squared. If it's plus 2ab, that factors to (a + b)(a + b) If it's minus 2ab, that factors to (a - b)(a - b)
What is trinomial perfect?
A trinomial is considered perfect if it can be expressed as the square of a binomial. For example, the trinomial (x^2 + 6x + 9) is a perfect square because it can be factored into ((x + 3)^2). Perfect trinomials typically take the form (a^2 + 2ab + b^2) or (a^2 - 2ab + b^2).
Why is the last term of a perfect square trinomial always positive?
This is related to the fact that the square of both a positive and a negative number is always positive. The last term is simply the square of the second term, in the original binomial.
Is the perfect square trinomial a product of the square of a binomial?
Yes. With w and z being any two numbers or variables: Take (w + z)2 = (w + z)(w + z) = ww + wz + zw + zz = w2 + 2wz + z2, which is the perfect square trinomial.
How do you factor the binomial 25x2-36y2?
25x2 - 36y2If you notice that 25 and 36 are perfect squares, you know that your answer would be like the following: (5_ + 6_)(5_ - 6_)because 25x2 - 36y2 is a perfect square binomial, so their square roots fit that way. This only works if the middle sign is minus.From there, you just plug in the x's and y's to get:(5x + 6y)(5x - 6y)
