Question

a8-47a⁴+1 factorise​

Answer 1

Step-by-step explanation:

Pulling out like terms :

2.1     Pull out like factors :

  a8 - a4  =   a4 • (a4 - 1)  

Trying to factor as a Difference of Squares :

2.2      Factoring:  a4 - 1  

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 : 1 is the square of 1

Check :  a4  is the square of  a2  

Factorization is :       (a2 + 1)  •  (a2 - 1)  

Answer 2

Step-by-step explanation:

a⁸+47a⁴+1

=a⁸+ 2a⁴+ 1 - 2a⁴ - 47a⁴ ( By adding and subtracting 2a4)

=[ (a⁴)²+2(a⁴)(1) + (1)²] - 49a⁴

=(a⁴+ 1)² - (7a²)²

= (a⁴+ 1 - 7a²)(a⁴+1+7a²)