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How Do You Factor a Polynomial Using Difference of Squares?

Factor 4x2-9 using the difference of squares

Summary

  1. The square root of 4, 2, is the coefficient in each of the first terms
  2. The square root of 9, 3, is the coefficient in each of the second terms
  3. In the first terms, we keep the same variable as before, x
  4. The new degree, 1 is half of the old degree, 2
  5. Check our answer by FOILing the two binomials back together

Notes

    1. We need to look for any common factors in our terms
    1. x is a variable
    1. Our first term, 4x2 has the factors 2, 2, x, and x
    2. Our second term, 9, has the factors 3 and 3
    3. Since none of these are the same, there is no greatest common factor
    1. The coefficient is the number, 4
    2. The variable is the letter, x
    3. The degree is the exponent, 2
    1. The coefficient is the number, 9
    2. The second term has no variable
    3. Since there is no variable, the degree is 0
    1. Remember, our coefficients are 4 and 9
    2. The square root of 4 is 2
    3. The square root of 9 is 3
    4. 2 and 3 are both whole numbers
    1. The square root of 4 is 2
    2. The square root of 9 is 3
    3. 2 and 3 are both whole numbers
    1. Remember, our degrees were 2 and 0
    2. These ARE both even numbers
    1. In difference of squares, we are always multiplying an addition by a subtraction
    1. Remember, our degrees were 2 and 0
    1. Remember, our degrees were 2 and 0
    2. Half of 2 is 1
    3. Half of 0 is 0
    1. Half of 2 is 1
    1. This is the degree of the variables in our first terms
    1. Anything to the 0 power is 1, so we don't have a variable in the second term
    1. We can check our answer by FOILing our binomials back together
    2. Remember, FOIL is a method we use to multiply together two binomials
    1. We can check our answer by FOILing our binomials back together
    2. Remember, FOIL is a method we use to multiply together two binomials
    1. Multiply the two FIRST terms, 2x•2x, to get 4x2
    2. Multiply the two OUTER terms, 2x•-3, to get -6x
    3. Multiply the two INNER terms, 3•2x, to get 6x
    4. Multiply the two LAST terms, 3•-3, to get -9
    1. -6x and 6x are like terms, because they both have x to the first power
    2. -6x+6x=0
    3. So the two terms cancel each other out