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Factoring a Difference of Squares

Factoring a Difference of Squares. Essential Question. How do I factor binomials using difference of squares?. Give these a try. Multiply. 4(j + 6) (n – 9)(n + 9) (2t + 5)(2t + 5) Solutions: 4j + 24 n 2 –81 4t 2 +20t +25. Definition. Perfect Squares :

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Factoring a Difference of Squares

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  1. Factoring a Difference of Squares

  2. Essential Question • How do I factor binomials using difference of squares?

  3. Give these a try • Multiply. • 4(j + 6) • (n – 9)(n + 9) • (2t + 5)(2t + 5) • Solutions: • 4j + 24 • n2 –81 • 4t2 +20t +25

  4. Definition • Perfect Squares: • What you get after you multiply something times itself. • For example: • 0, 1, 4, 9, 16, 25, etc. • Is x2 a perfect square? • What about x4y6z8? YES YES

  5. Difference of Squares • For all numbers a and b: a2 – b2 = (a + b)(a – b)

  6. Ex. 1) Factor 4a2 – 25b2 • First…ALWAYS try to factor out a GCF! • We can’t • Are both of these terms perfect squares? • Is there a minus sign in the middle? • Then use “difference of squares”. • (2a + 5b)(2a – 5b)

  7. Ex. 2) Factor 36x4 - 9y2 • Is there a GCF? • Yes • 9(4x4 – y2) • Are both terms left in the parentheses perfect squares? • Is there a minus sign between the terms? • Factor using a difference of squares! • 9(2x2 – y)(2x2 + y)

  8. Ex. 3) Factor -49 + a4 • First rewrite in standard form! • a4 – 49 • Now we can factor the difference of squares! • (a2 – 7)(a2 + 7)

  9. Ex. 4) Factor 16r2 + 49 • Is there a GCF? • NO …. • Are both terms perfect squares? • Yes • Is there a minus sign in the middle? • NO! • Can’t factor using difference of squares. • Must be PRIME

  10. Ex. 5) Factor 25n2 – 100 • What should you always ask yourself FIRST??? • GCF • 25 (n2 – 4) • 25(n + 2)(n – 2) • MUST DO GCF FIRST!!

  11. Ex. 6) Factor 16x2 – 49x4 • GCF??? YES! • x2(16-49x2) • x2(4-7x)(4+7x)

  12. Practice Factor Completely! • x2 – 4 • 36a2 – 49b2 • 25w2x4 – 81y2 • (x + 2)(x – 2) • (6a + 7b)(6a – 7b) • (5wx2 + 9y)(5wx2 – 9y)

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