Question

16 m^4 -81 n^4 factorise it​

Answer 1

Step-by-step explanation:

Factoring: 16m4-n4

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 : 16 is the square of 4

Check : m4 is the square of m2

Check : n4 is the square of n2

Factorization is : (4m2 + n2) • (4m2 - n2)

Trying to factor as a Difference of Squares:

2.2 Factoring: 4m2 - n2

Check : 4 is the square of 2

Check : m2 is the square of m1

Check : n2 is the square of n1

Factorization is : (2m + n) • (2m - n)

Final result :

(4m2 + n2) • (2m + n) • (2

That's all