Difference of 2 Squares and Perfect Square Trinomials

Difference of 2 Squares and Perfect Square Trinomials

Factoring Day 1 GCF Difference of 2 Squares factor by grouping GCF Find the Greatest Common Factor Example 1 Example 3 Example 5 3 2 2 2 2 5a 15 6k 10k Example 2 2 Example 4 3

3n 9n 6a 18ab 3a b 15ab 3 GCF Find the Greatest Common Factor Example 1 2 5a 15 5 a 2 3

GCF Find the Greatest Common Factor Example 2 2 3n 9n 3n n 3 GCF Find the Greatest Common Factor Example 3 3 6k 10k 2 2k 3k 5 2

GCF Find the Greatest Common Factor Example 4 3 6a 18ab 6a a 3b 2 GCF Find the Greatest Common Factor Example 5 2 2 3a b 15ab 2 3ab a 5b 3

Difference of 2 Squares 1.Is there a GCF? 2. Are there only 2 terms? 3. Is it a difference? (subtraction) 4. Are they both perfect squares? Perfect Squares 2 1 4 64 9 81 16 100

25 121 36 144 49 x 4 x x 6 x 8

10 x Difference of 2 Squares Example 6 2 x 9 ( x 3) ( x 3) 2 x 3x 3x 9 2 x 9 1. Is there a GCF? 2. Are there only 2 terms? 3.

Is it a difference? (subtraction) 4. Are they both perfect squares? Factor 2 2x 8 2 2( x 4) 2( x 2)( x 2) Example 7 Factor 2

9x 1 Example 8 (3 x 1) (3 x 1) Factor 4 x 16 2 Example 9 2 ( x 4) ( x 4) 2 ( x 4) ( x 2) ( x 2)

Factoring Flow Chart How many terms? 2 terms? 3 terms ? Difference of 2 squares ? Yes factor Is there a GCF ? 4 terms ? Can you factor

by grouping? No STO P Split the Middle Factor by Grouping 1. Splitting the problem up 2. Factor common monomials from each group using the GCF 3. Factor out the common binomial 4. Factor the difference of squares and GCF 5. Check EXAMPLE 10 Factor out GCF Group Terms

3 x 3x 4 x 12 Factor non e Factor common monomials Factor out common binomial Factor the difference of squares 2 3 2 x 3x 4 x 12

x3 3x 2 4 x 12 x 2 ( x 3) 4( x 3) 2 x 3 x 4 ( x 3)( x 2)( x 2) EXAMPLE 11

Facto r 2 2x 4x 4x 8 Factor out GCF 2 x 2x 2x 4 Group Terms 2 x 2 x 2 x 4 2 2 Factor common monomials 2 x x 2 2 x 2

Factor out common binomial 2 x 2 x 2 Factor the difference of squares or check GCF 2( x 2)( x 2) 3 2 Factor x x 2x 2 EXAMPLE 12 Factor GCF none

Group Terms Factor common monomials Factor out common binomial Factor the difference of squares or check CGF 3 2 x x 2 x 2. x 3 x 2

2 x 2 2 x ( x 1) 2 ( x 1) x 1 x 2 x 1 x 2 2 2 EXAMPLE 13 Factor x x 25 x 25. 3 Factor GCF none Group Terms Factor common

monomials Factor out common binomial Factor the difference of squares or check GCF 2 3 2 3 2 x x 25 x 25 x x

25x 25 2 x ( x 1) 25( x 1) x 1 x 2 25 ( x 1)( x 5)( x 5)

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