Question

simplify (a2-b2) (a2+b2) - (a2-b2)2​

Answer 1

Answer:

(a²-b²)(a²+b²)-(a²-b²)²

using identity: (a-b)(a+b)=a²-b²

[(a²)²-(b²)²]-(a²-b²)²

[a⁴-b⁴]-(a²-b²)²

using identity : (a-b)²=a²+b²-2ab

[a⁴-b⁴]-[(a²)²+(b²)²-2×a²×b²

a⁴-b⁴-[a⁴+b⁴-2a²b²]

a⁴-b⁴-a⁴-b⁴+2a²b²

2a²b²-2b⁴

2b²(a²-b²)

Answer 2

$( {a}^{2} - {b}^{2} ) ( {a}^{2} + {b}^{2} ) - {( {a}^{2} - {b}^{2} )}^{2} \\ ( {a}^{2} - {b}^{2} )({a}^{2} + {b}^{2} - {a}^{2} + {b}^{2} ) \\ ( {a}^{2} - {b}^{2} )(2 {b}^{2} ) = (a + b)(a - b)(2 {b}^{2} )$

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