Question

factorise (625x^8-1)​

Answer 1

$\huge\underline\mathfrak\red{Answer}$

$625x {}^{8} - 1 \\ \\ (25 { x}^{4} - 1) \times (25 {x}^{4} + 1) \\ \\ (5x {}^{2} - 1) \times (5 {x}^{2} + 1) \times (25x {}^{4} + 1)$

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Answer 2

Helo mate here your ans

625x8-1

Final result :

(25x4 + 1) • (5x2 + 1) • (5x2 - 1)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

54x8 - 1

Step 2 :

Trying to factor as a Difference of Squares :

2.1 Factoring: 625x8-1

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 : 625 is the square of 25

Check : 1 is the square of 1

Check : x8 is the square of x4

Factorization is : (25x4 + 1) • (25x4 - 1)

Thanks