Factoring the following binomials using get andor sum or dif

Factoring the following binomials using get and/or sum or difference of squares.

Solution

1. y² - 16 = y² - (4)² = (y + 4)(y - 4) [ as a² - b² = (a +b) (a - b) ]

2. 49y² - 16z² = (7y)² - (4z)² = (7y + 4z) (7y - 4z)

3. 25y² - 121 = (5y)² - (11)² = (5y + 11) (5y - 11)

4. 64b² - 36c² = (8b)² - (6c)² = (8b + 6c)(8b - 6c)

5. 81b⁴ - 16c⁴ = (9b²)² - (4c²)² = (9b² + 4c²) (9b² - 4c²) = (9b² + 4c²)[ (3b)² - (2c)² ] =   (9b² + 4c²)(3b + 2c)(3b - 2c)

6. 64b² + c² No factorization is possible.

7. 9b⁴ - 81c² = (3b²)² - (9c)² = (3b² + 9c)( 3b² - 9c)

8. 2b² -50c² = 2[ b² - (5c)² ] = 2 (b+ 5c) (b - 5c)

9. 64b² + 36c² No factorization is possible.

10. 27b⁴ - 3y² = 3( 9b⁴ - y²) = 3 [ (3b²)² - y² ] = 3 ( 3b² + y)(3b² - y)