Factorize:
x(x–2)(x–4)+4x-8
Answers
The expression is given as : x(x – 2) (x – 4) + 4x – 8
Here , in the given expression 4 is common factor in 4x – 8 :
= x(x – 2) (x – 4) + 4(x – 2)
Taking (x - 2) common factor :
= (x – 2) [x (x – 4) + 4]
= (x – 2) (x² – 4x + 4)
= (x – 2) [x² – 2 (x) (2) + (2)²]
By using the identity a² - 2ab + b² = (a - b)² :
= (x – 2) (x – 2)²
= (x – 2)³
Hence, the factorisation of x(x – 2) (x – 4) + 4x – 8 is (x – 2)³.
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Answer:
Step-by-step explanation:
Taking (x - 2) common factor :
= (x – 2) [x (x – 4) + 4]
= (x – 2) (x² – 4x + 4)
= (x – 2) [x² – 2 (x) (2) + (2)²]
By using the identity a² - 2ab + b² = (a - b)² :
= (x – 2) (x – 2)²
= (x – 2)³
Hence, the factorisation of x(x – 2) (x – 4) + 4x – 8 is (x – 2)³.