Question

A4 - 81 factorise solutions

Answer 1

Hey mate!!

$A^{4} - 81\\ =( A^{2} )^{2} - 9^{2} \\ => x^{2} - y^{2} = (x-y)(x+y)\\ = (A-9)(A+9)$

That's the answer.

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Answer 2

Given:

An expression A^4 - 81.

To Find:

The above expression in factors form.

Solution:

The given problem can be solved using the formula a²-b².

1. The given expression is$(A^4-81)$,

2. Consider the term (a²-b²), It can be also written as,

=>  (a²-b²) = ( a+b ) x ( a-b ),

3. Use the above formula in the given equation.

=>  A^4 - 81 = (A² + 9) x (A² - 9),

4. The term (A² - 9) can be expanded using the same formula,

=> (A² - 9) = (A + 3) x (A - 3),

5. Therefore, the term$(A^4-81)$ can be written into simpler terms as,

=> $(A^4-81)$ = (A² + 9) x (A + 3) x (A - 3).

Therefore, the term$(A^4-81)$ after factorising can be written as (A² + 9) x (A + 3) x (A - 3).