Question

factorise a^16 b^4 - a^4 b^16​

Answer 1

Answer:

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 : a12 is the square of a6

Check : b12 is the square of b6

Factorization is : (a6 + b6) • (a6 - b6)

Trying to factor as a Sum of Cubes:

2.3 Factoring: a6 + b6

Theory : A sum of two perfect cubes, a3 + b3 can be factored into :

(a+b) • (a2-ab+b2)

Proof : (a+b) • (a2-ab+b2) =

a3-a2b+ab2+ba2-b2a+b3 =

a3+(a2b-ba2)+(ab2-b2a)+b3=

a3+0+0+b3=

a3+b3

Check : a6 is the cube of a2

Check : b6 is the cube of b2

Factorization is :

(a2 + b2) • (a4 - a2b2 + b4)

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Answer 2

Answer:

Step-by-step explanation: