Question

49x^4-16y^4. factorise the following expression .​

Answer 1

Answer:

 (7x2 + 4y2)  •  (7x2 - 4y2) 

Step-by-step explanation:

Factoring:  49x4-16y4 

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 :  49  is the square of  7 

Check : 16 is the square of 4

Check :  x4  is the square of  x2 

Check :  y4  is the square of  y2 

Factorization is :       (7x2 + 4y2)  •  (7x2 - 4y2)