Question

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

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Answer 1

Answer:

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

2. $2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)$

Step-by-step explanation:

1. $a^{8} - {b}^{8}$

➡️ $( {a}^{4} - {b}^{4} ) \times ( {a}^{4} + {b}^{4} )$

➡️ $( {a}^{2} - {b}^{2} ) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )$

➡️ $(a - b) \times (a + b) \times ( {a}^{2} + {b}^{2} ) \times ( {a}^{4} + {b}^{4} )$

➡️ $2(16 {y}^{4} - 81)$ ✅

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2. $32 {y}^{4} - 162$

➡️ $2(16y^{4} - 81)$

➡️ $2(4 {y}^{2} - 9) \times (4 {y}^{2} + 9)$

➡️ $2(2y - 3) \times (2y + 3) \times (4 {y}^{2} + 9)$ ✅