what is a perfect square trinomial in math A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression It is of the form ax 2 bx c Here a b and c are real numbers and a 0 For example let us take a binomial x 4 and multiply it to x 4 The result obtained is x 2 8x 16
This means that the polynomial is a perfect square trinomial We can factor it as follows x 4 2 x 2 1 x 2 2 2 x 2 1 1 2 x 2 1 2 It means the trinomial latex x 2 8x 16 latex fits the requirements of a perfect square trinomial Since the middle term of the trinomial is positive the middle term of the binomial will also be positive Thus we can use the formula below to factor the trinomial
what is a perfect square trinomial in math
what is a perfect square trinomial in math
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An expression is said to a perfect square trinomial if it takes the form ax 2 bx c and satisfies the condition b 2 4ac The perfect square formula takes the following forms ax 2 2abx b 2 ax b 2 ax 2 2abx b 2 ax b 2 Example 1 Perfect Square Trinomial An expression that is obtained from the square of a binomial is termed a perfect square trinomial For example if we square the expression y 3 we use the identity a b 2 a 2 2ab b 2 and we get y 3 2 y 2 6y 9 Here y 2 6y 9 is a perfect square trinomial
This lesson explains the perfect square trinomial and how to find the perfect square trinomial using a formula Also see perfect square trinomial examples Updated 11 21 2023 A perfect square trinomial is a special form of quadratic trinomial that can be factored into a binomial squared a x b 2 or a x b 2 It arises when you square a binomial resulting in a trinomial where The first term is a perfect square The third term is also a perfect square
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About Transcript When an expression has the general form a 2ab b then we can factor it as a b For example x 10x 25 can be factored as x 5 This method is based on the pattern a b a 2ab b which can be verified by expanding the parentheses in a b a b Questions Tips Thanks Want to join the conversation Log in Sort by The pattern for a perfect square trinomial is a 2x 2 2abx b 2 Sal is factoring 25x 2 30x 9 He uses the middle term from the pattern and from his trinomial to get 2ab 30 If you divide both sides by 2 you get ab 15 Hope this helps
Perfect square trinomials are of the form a2x2 2 axb b2 and are expressed in squared binomial form as ax b 2 How does this look in practice Is x2 10x 25 a perfect square trinomial If so write the trinomial as the square of a binomial Well the first term x2 is the square of x The third term 25 is the square of 5 A Perfect Square Trinomial is a specific type of trinomial where two of the terms are perfect squares and the middle term is twice the product of the square roots of those perfect squares In other words it takes the form a 2ab b or a 2ab b It is like a magical formula that mathematicians and algebra lovers adore Properties of Trinomials
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what is a perfect square trinomial in math - Factoring Perfect Square Trinomials MathBitsNotebook A1 Notice the Pattern of the middle term The middle term is twice the product of the binomial s first and last terms a b middle term 2ab a b middle term 2ab In a b the last term is b