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Factoring ax 2 – c

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  1. Factoring ax2 – c Math 10

  2. LEQ: How can you factor differences of two squares? Vocabulary: -None!

  3. Introduction You are know going to factor a difference of squares. What operation does difference mean? Give me examples of squares. (Not the shape!) The new expression you should know is: ax2 - c

  4. Guided Notes Have your guided notes ready to fill in. Degree must be 2 with subtraction The number of terms is 2 Must be able to take the square root of “a” and “c”

  5. Steps to Factoring Success • Take the square root of the coefficient and the variable of the 1st term. Write your answer in your parentheses. ~Note: when you take the square root of a variable w/ exponents, just divide the exponent by 2. • Take the square root of the last term and write it as the last term in both parentheses • Make one a + and the other a – (minus)

  6. Factoring Difference of Squares Example: 81x2 – 36 ( ) ( ) √(81x2) = √(36) = - 9x + 6 9x 6 9x 6

  7. Factoring Difference of Squares Example: x2 – 81 ( ) ( ) √(x2) = √(81) = - x + 9 x 9 x 9

  8. Factoring Difference of Squares Example: 9x4 – 16q2 ( ) ( ) √(9x4) = √(16q2) = - 3x2 + 4q 3x2 4q 3x2 4q

  9. Factoring Difference of Squares Example: 1 – 4x2 ( ) ( ) √(1) = √(4x2) = - 1 + 2x 1 2x 1 2x

  10. Factoring Difference of Squares Example: m8 – 49 ( ) ( ) √(m8) = √(49) = - m4 + 7 m4 7 m4 7

  11. Factoring Difference of Squares Example: 100x2 – 4y2 ( ) ( ) √(100x2) = √(4y2) = - 10x + 2y 10x 2y 10x 2y

  12. Factoring Difference of Squares Example: x4 – 25y6 ( ) ( ) √(x4) = √(25y6) = x2 + 5y3 x2 - 5y3 x2 5y3