Difference+of+squares

=‍‍= DIFFERENCE OF SQUARES Difference of squares always has two terms in the polynomial. The two numbers in the binomial have to be perfect squares, if not the the equation wouldn't work. Perfect squares are a number times themselves One example is 9. 9 is 3 X 3.

The two terms must be seperated by a subtraction sign. One example of difference of squares is (a 2 - b 2 ). There are two terms, Both are perfect squares, and they are seperated by a subtraction sign.

But what is the quadratic factored out to be? In difference of squares there is no middle term because the two products of the middle term cancel out. Lets test this out. To factor out this example find the square root of both terms. square root of a 2 is a, and the square root of b 2 is b. The sign seperating the two terms is a subtraction sign so there has to be a positive and a negative sign in both binomial terms. so it should like this before you substitute in your numbers, ( + )( - ). Now put in the two square roots you found earlier into both terms, you should have something like this (a+b)(a-b) Now if we FOIL this out it looks like a 2 + ab - ab - b 2, The two middle terms cancel out and you get (a 2 - b 2 ). Another example is (25x 2 - 100)

This example has two terms, seperated by a subtraction sign, and they both terms are perfect squares. The square root of 25x 2 is 5x, and the square root of 100 is 10. So when we set up the to binomials it will look like this, ( + )( - ). Subtitute the 5x in the spot before the signs and it will look like this, (5x+ )(5x- ). Then substitute the 10 in the spot after the signs,now you have the factored quadratic and it looks like the, (5x+10)(5x-10).

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