A3 - Polynomials

# 4 m 2 n 6 4 m 2 n 6 math 17 inst of mathematics

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= (4 m 2 + n 6 )(4 m 2 - n 6 ) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 22 / 30

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Difference of Two Squares x 2 - y 2 = ( x + y )( x - y ) Examples: 1 4 a 2 - b 2 = (2 a ) 2 - ( b ) 2 = (2 a + b )(2 a - b ) 2 16 m 4 - n 12 = (4 m 2 ) 2 - ( n 6 ) 2 = (4 m 2 + n 6 )(4 m 2 - n 6 ) = (4 m 2 + n 6 )(2 m + n 3 )(2 m - n 3 ) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 22 / 30
Perfect Square Trinomial x 2 ± 2 xy + y 2 = ( x ± y ) 2 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 23 / 30

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Perfect Square Trinomial x 2 ± 2 xy + y 2 = ( x ± y ) 2 Examples: 1 4 a 2 + 4 ab + b 2 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 23 / 30
Perfect Square Trinomial x 2 ± 2 xy + y 2 = ( x ± y ) 2 Examples: 1 4 a 2 + 4 ab + b 2 = (2 a ) 2 + 2 · 2 a · b + b 2 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 23 / 30

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Perfect Square Trinomial x 2 ± 2 xy + y 2 = ( x ± y ) 2 Examples: 1 4 a 2 + 4 ab + b 2 = (2 a ) 2 + 2 · 2 a · b + b 2 = (2 a + b ) 2 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 23 / 30
Perfect Square Trinomial x 2 ± 2 xy + y 2 = ( x ± y ) 2 Examples: 1 4 a 2 + 4 ab + b 2 = (2 a ) 2 + 2 · 2 a · b + b 2 = (2 a + b ) 2 2 121 m 4 - 44 m 2 n 4 + 4 n 8 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 23 / 30

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Perfect Square Trinomial x 2 ± 2 xy + y 2 = ( x ± y ) 2 Examples: 1 4 a 2 + 4 ab + b 2 = (2 a ) 2 + 2 · 2 a · b + b 2 = (2 a + b ) 2 2 121 m 4 - 44 m 2 n 4 + 4 n 8 = (11 m 2 ) 2 - 2 · 11 m 2 · 2 n 4 + (2 n 4 ) 2 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 23 / 30
Perfect Square Trinomial x 2 ± 2 xy + y 2 = ( x ± y ) 2 Examples: 1 4 a 2 + 4 ab + b 2 = (2 a ) 2 + 2 · 2 a · b + b 2 = (2 a + b ) 2 2 121 m 4 - 44 m 2 n 4 + 4 n 8 = (11 m 2 ) 2 - 2 · 11 m 2 · 2 n 4 + (2 n 4 ) 2 = (11 m 2 - 2 n 4 ) 2 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 23 / 30

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Factoring Polynomials Sum and Difference of Two Cubes x 3 ± y 3 = ( x ± y )( x 2 xy + y 2 ) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 24 / 30
Factoring Polynomials Sum and Difference of Two Cubes x 3 ± y 3 = ( x ± y )( x 2 xy + y 2 ) Examples: z 3 + 125 = ( z ) 3 + (5) 3 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 24 / 30

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Factoring Polynomials Sum and Difference of Two Cubes x 3 ± y 3 = ( x ± y )( x 2 xy + y 2 ) Examples: z 3 + 125 = ( z ) 3 + (5) 3 = ( z + 5) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 24 / 30
Factoring Polynomials Sum and Difference of Two Cubes x 3 ± y 3 = ( x ± y )( x 2 xy + y 2 ) Examples: z 3 + 125 = ( z ) 3 + (5) 3 = ( z + 5)( z 2 - 5 z + 25) Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 24 / 30

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Factoring Polynomials Sum and Difference of Two Cubes x 3 ± y 3 = ( x ± y )( x 2 xy + y 2 ) Examples: z 3 + 125 = ( z ) 3 + (5) 3 = ( z + 5)( z 2 - 5 z + 25) 27 - 64 m 3 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 24 / 30
Factoring Polynomials Sum and Difference of Two Cubes x 3 ± y 3 = ( x ± y )( x 2 xy + y 2 ) Examples: z 3 + 125 = ( z ) 3 + (5) 3 = ( z + 5)( z 2 - 5 z + 25) 27 - 64 m 3 = (3) 3 - (4 m ) 3 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 24 / 30

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Factoring Polynomials Sum and Difference of Two Cubes x 3 ± y 3 = ( x ± y )( x 2 xy + y 2 ) Examples:

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