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How Do You Know if You Have a Difference of Squares?

How to identify a difference of squares problem

Summary

  1. 'Difference' means subtraction
  2. 4x2-9 is an example of a difference of squares
  3. The two terms are 4x2 and 9
  4. A perfect square gives a whole number when you take its square root
  5. 4 and 9 are the coefficients of our terms
  6. The square root of 4 is 2 and the square root of 9 is 3
  7. The degree is the sum of all the exponents of a term
  8. The degree of 4x2 is 2 and the degree of 9 is 0

Notes

    1. 'Difference of squares' means we will be subtracting two perfect squares
    1. 4x2 and 9 are two perfect squares that are being subtracted
    1. 4x2 and 9 are the terms of this polynomial
    1. 4x2 and 9 are the terms of this polynomial
    1. 4x2 and 9 are the terms of this polynomial
    1. A perfect square is a number that gives a whole number when you take the square root
    1. A perfect square is a number that gives a whole number when you take the square root
    1. Our coefficients are 4 and 9
    1. 4 is the same as 2•2, or 22
    2. So 4 is a perfect square
    1. 4 is the same as 2•2, or 22
    2. So 4 is a perfect square
    1. 9 is the same as 3•3, or 32
    2. So 9 is a perfect square
    1. 9 is the same as 3•3, or 32
    2. So 9 is a perfect square
    1. We are looking for a DIFFERENCE of squares
    2. Since 'difference' means subtraction, we need a MINUS sign between our terms
    1. We are looking for a DIFFERENCE of squares
    2. Since 'difference' means subtraction, we need a MINUS sign between our terms
    1. We are subtracting 4x2 and 9, so we have a difference
    1. The degree of a monomial or term is just the sum of all the exponents of all the variables of that term
    1. Our terms are 4x2 and 9
    1. The exponent on x is 2, so its degree is 2
    2. Since 2 is EVEN, it fits the characteristic
    1. Not having a variable is the same as having a variable to the 0 power, since anything to the 0 power is 1
    1. Anything to the 0 power is 1
    1. So 9 has a degree of 0
    1. Both of our terms have degrees that are even or zero, since 2 is even and 0 is zero