Difference Of Two Square
Polynomials which are in the form of the difference of two squares can be factorized by using the following relations => a² -b² = ( a + b ) ( a – b )
Example.1) Factorized 49a² - 36b²
Ans.) 49a² - 36b² = ( 7a + 6b ) ( 7a – 6b )
Example.2) Factorize a²- ( b + c )²
Ans.) a² - ( b + c )²
= { a – ( b + c )} { a + ( b + c )}
= ( a – b – c ) ( a + b + c )
Example-3) Factorize a⁴ - b⁴
Ans.) a⁴ - b⁴ = ( a² + b² ) ( a² - b² )
= ( a² + b² ) ( a + b ) ( a – b )
Example.4) Factorize (0.30 )⁴ - (0.20)⁴
Ans.) (0.30 )⁴ - (0.20)⁴
= {(0.30 )² + (0.20)²} {(0.30 )² - (0.20)²}
= {(0.30 )² + (0.20)²} ( 0.30 + 0.20 ) ( 0.30 – 0.20 )
= ( 0.09 + 0.04 ) ( 0.50 ) ( 0.10 )
= ( 0.13 ) X ( 0.05)
= 0.0065 (Ans.)