Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring The Difference of Squares Difference of Squares x 2 – y 2 = ( x + y )( x – y )

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 1Factoring Differences of Squares Factor each polynomial. (a) 2 n 2 – 50

Copyright © 2010 Pearson Education, Inc. All rights reserved. 7.3 Special Factoring EXAMPLE 1Factoring Differences of Squares Factor each polynomial. (b) 9 g 2 – 16 (c) 4 h 2 – ( w + 5) 2

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring Caution CAUTION Assuming no greatest common factor except 1, it is not possible to factor (with real numbers) a sum of squares, such as x

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 2Factoring Perfect Square Trinomials Factor each polynomial. (a) 9 g 2 – 42 g + 49

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 2Factoring Perfect Square Trinomials Factor each polynomial. (b) 25 x xy + 64 y 2

Special Factoring EXAMPLE 2Factoring Perfect Square Trinomials Factor each polynomial. (d) c 2 – 6 c + 9 – h 2

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring Difference of Cubes x 3 – y 3 = ( x – y )( x 2 + xy + y 2 )

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Special Factoring Sum of Cubes x 3 + y 3 = ( x + y )( x 2 – xy + y 2 )

Special Factoring EXAMPLE 3Factoring Difference of Cubes Factor each polynomial. Recall, x 3 – y 3 = ( x – y )( x 2 + xy + y 2 ). (a) a 3 – 125

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 4Factoring Sums of Cubes Factor each polynomial. Recall, x 3 + y 3 = ( x + y )( x 2 – xy + y 2 ). (a) n (b) 64 v g 3

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 3Factoring Difference of Cubes Factor each polynomial. Recall, x 3 – y 3 = ( x – y )( x 2 + xy + y 2 ). (b) 8 g 3 – h 3

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 3Factoring Difference of Cubes Factor each polynomial. Recall, x 3 – y 3 = ( x – y )( x 2 + xy + y 2 ). (c) 64 m 3 – 27 n 3

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring EXAMPLE 4Factoring Sums of Cubes Factor each polynomial. Recall, x 3 + y 3 = ( x + y )( x 2 – xy + y 2 ). (c) 2 k =

Copyright © 2010 Pearson Education, Inc. All rights reserved. Special Factoring Factoring Summary Special Types of Factoring (Memorize) Difference of Squares x 2 – y 2 = ( x + y )( x – y ) Difference of Cubes x 3 – y 3 = ( x – y )( x 2 + xy + y 2 ) Sum of Cubes x 3 + y 3 = ( x + y )( x 2 – xy + y 2 )