Question

Factorize the following questions
1. a^8-b^8
2. 32y^4 - 162

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Answer 1

1.
`2(16 {y}^(4) - 81)`

2.
`2(2y - 3) * (2y + 3) * (4 {y}^(2) + 9)`

Explanation:

1.
`a^(8) - {b}^(8)`

➡️
`( {a}^(4) - {b}^(4) ) * ( {a}^(4) + {b}^(4) )`

➡️
`( {a}^(2) - {b}^(2) ) * ( {a}^(2) + {b}^(2) ) * ( {a}^(4) + {b}^(4) )`

➡️
`(a - b) * (a + b) * ( {a}^(2) + {b}^(2) ) * ( {a}^(4) + {b}^(4) )`

➡️
`2(16 {y}^(4) - 81)` ✅

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2.
`32 {y}^(4) - 162`

➡️
`2(16y^(4) - 81)`

➡️
`2(4 {y}^(2) - 9) * (4 {y}^(2) + 9)`

➡️
`2(2y - 3) * (2y + 3) * (4 {y}^(2) + 9)` ✅