factor the expression 81x^2-54xy+9y^2 into product of binominials
81x^2 - 54xy + 9y^2
9(9x^2 - 6xy + y^2)
9(3x - y)(3x - y)
9(3x - y)^2
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81x^2-54xy+9y
To factor the expression 81x^2 - 54xy + 9y^2 into a product of binomials, you can follow these steps:
Step 1: Identify if there is a common factor between all the terms. In this case, all three terms have a common factor of 9. So, we can factor out 9 from each term:
9(9x^2 - 6xy + y^2)
Step 2: Now, the expression inside the parentheses is a perfect square trinomial. To factor a perfect square trinomial, we take the square root of the first term and the square root of the last term to form the binomials.
The square root of 9x^2 is 3x, and the square root of y^2 is y:
9(3x - y)(3x - y)
Step 3: Since we have the same binomial, we can write it with a squared exponent:
9(3x - y)^2
So, the fully factored expression is 9(3x - y)^2.