# CLASS-8ALGEBRAIC FACTORIZATION - DIFFERENCE OF TWO SQUARE

Difference of Two Square

The difference of two squares can always be factorized by the formula -   a²- b²= (a+b)(a-b)

Example.1)  Factorize 25a² - 16b²

Ans.)  As we know that,  25a² = (5a)² and  16b² = (4b)²

So,  25a²- 16b² = (5a)²- (4b)² = (5a+4b)(5a-4b)       (Ans.)

Example.2)  Factorize 3a²- 27b²

Ans.) The HCF of the numerical coefficients in the two terms = 3, so, we take 3 out as the common factor

As we know,  a² = (a)² and  9b² = (3b)²

So, 3a²- 27b² = 3(a²- 9b²) =  3{(a)² - (3b)²}

=  3 (a+3b)(a-3b)       (Ans.)

Example.3) Factorize  9(a+b)² - 25(x-y)²

Ans.)  9(a+b)²- 25(x-y)² = {3(a+b)}²- {5(x-y)}²

=  {3(a+b) + 5(x-y)} {3(a+b) - 5(x-y)}

=  (3a+3b+5x-5y) (3a+3b-5x+5y)     (Ans.)

Example.4)  Factorize 16x²- y²+ 10y – 25

Ans.)   16x²- y² + 10y – 25

=   16x² - (y² - 10y + 25)

=   16x² - {y² - 2.y.5 + (5)²}

=  16x² - (y-5)²  =  (4x)² - (y-5)²

= (4x+y-5)(4x-y+5)       (Ans.)

Example.5)  Factorize  2x⁴ - 32y⁴

Ans.)        2x⁴ - 32y⁴

= 2 (x⁴ - 16y⁴) = 2{(x²)²- (4y²)²}

= 2{(x² + 4y²) (x²- 4y²)}

=  2(x²+4y²) {(x)² - (2y)²}

=  2(x²+4y²) (x+2y)(x-2y)         (Ans.)