Question

please solve anyone.......

Answer 1

Here is your answer----
$\frac{ {a}^{4} - {b}^{4} }{ {a}^{2} - ab } \\ \frac{ {(( {a)}^{2}) }^{2} - {( ({b)}^{2}) }^{2} }{a(a - b)} \\ \frac{ ({a}^{2} - {b}^{2} )( {a}^{2} + {b}^{2} ) }{a(a - b)} \\ \frac{(a + b)(a - b)( {a}^{2} + {b}^{2}) }{a(a - b)} \\ \frac{(a + b)( {a}^{2} + {b}^{2} ) }{a}$
Hope it will help you.

Answer 2

(a⁴-b⁴)/(a²-ab)

Simplify

a⁴ - b⁴/a²- ab

Pull out like factors :

a² - ab  =   a • (a - b)

Factoring:  a⁴ - b⁴

Theory :

A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :

(A+B) • (A-B) =

        A² - AB + BA - B² =

        A² - AB + AB - B² =  

        A² - B²

Note :  AB = BA is the commutative property of multiplication.  

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  a⁴  is the square of  a²  

Check :  b⁴  is the square of  b²  

Factorization is :       (a² + b²)  •  (a² - b²)

Factoring:  a² - b²

Check :  a²  is the square of  a¹

Check :  b²  is the square of  b¹  

Factorization is :       (a + b)  •  (a - b)

Cancel out  (a - b)  which appears on both sides of the fraction line.

(a² + b²) • (a + b)/a        

Ans

(a² + b²) • (a + b)/a