Perfect square trinomial generally has the pattern of a2 + 2ab + b2or a2 - 2ab + b2. Given a binomial, to find the perfect square trinomial, we follow the steps given below. They are,
Step 1: Find the square the first term of the binomial.
Step 2: Multiply the first and the second term of the binomial with 2.
Step 3: Find the square of the second term of the binomial.
Step 4: Sum up all the three terms obtained in steps 1, 2, and 3.
The first term of the perfect square trinomial is the square of the first term of the binomial. and the second term is twice the product of the two terms of the binomial and the third term is the square of the second term of the binomial. Take a look at the figure shown below to understand the perfect square trinomial pattern. If the binomial being squared has a positive sign, then all the terms in the perfect square trinomial are positive, whereas, if the binomial has a negative sign attached with its second term, then the second term of the trinomial (which is twice the product of the two variables) will be negative.
How to Factor Perfect Square Trinomial?
Perfect square trinomials are either separated by a positive or a negative symbol between the terms. Two important algebraic identities with regards
(a - b)2 = a2 - 2ab + b2
The steps to be followed to factor a perfect square polynomial are as follows.
Write the given perfect square trinomial of the form a2 + 2ab + b2 or a2 - 2ab + b2, such that the first and the third terms are perfect squares, one being a variable and another being a constant.
Check if the middle term is twice the product of the first and the third term. Also, check the sign of the middle term.
If the middle term is positive, then compare the perfect square trinomial with a2 + 2ab + b2 and if the middle term is negative, then compa
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Answer:
Perfect square trinomial generally has the pattern of a2 + 2ab + b2or a2 - 2ab + b2. Given a binomial, to find the perfect square trinomial, we follow the steps given below. They are,
Step 1: Find the square the first term of the binomial.
Step 2: Multiply the first and the second term of the binomial with 2.
Step 3: Find the square of the second term of the binomial.
Step 4: Sum up all the three terms obtained in steps 1, 2, and 3.
The first term of the perfect square trinomial is the square of the first term of the binomial. and the second term is twice the product of the two terms of the binomial and the third term is the square of the second term of the binomial. Take a look at the figure shown below to understand the perfect square trinomial pattern. If the binomial being squared has a positive sign, then all the terms in the perfect square trinomial are positive, whereas, if the binomial has a negative sign attached with its second term, then the second term of the trinomial (which is twice the product of the two variables) will be negative.
How to Factor Perfect Square Trinomial?
Perfect square trinomials are either separated by a positive or a negative symbol between the terms. Two important algebraic identities with regards
(a - b)2 = a2 - 2ab + b2
The steps to be followed to factor a perfect square polynomial are as follows.
Write the given perfect square trinomial of the form a2 + 2ab + b2 or a2 - 2ab + b2, such that the first and the third terms are perfect squares, one being a variable and another being a constant.
Check if the middle term is twice the product of the first and the third term. Also, check the sign of the middle term.
If the middle term is positive, then compare the perfect square trinomial with a2 + 2ab + b2 and if the middle term is negative, then compa