Question

a⁴-b⁴
please give me answer​

Answer 1

Answer:

(a

2

+

2

ab+b

2

)(a

2

−

2

ab+b

2

)

Step-by-step explanation:

a^4 + b^4 = (a^2)^2 + (b^2)^2a

4

+b

4

=(a

2

)

2

+(b

2

)

2

∵ (x + y)² = x² + 2xy + y² ⇒ x² + y² = (x + y)² - 2xy,

\implies a^4 + b^4 = (a^2 + b^2)^2 - 2a^2b^2⟹a

4

+b

4

=(a

2

+b

2

)

2

−2a

2

b

2

=(a^2 + b^2)^2 - 2a^2b^2=(a

2

+b

2

)

2

−2a

2

b

2

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

2

+b

2

)

2

−(

2

ab)

2

By using x² - y² = (x + y)(x-y),

We get,

a^4 + b^4 = (a^2 + b^2 +\sqrt{2}ab)(a^2 + b^2 -\sqrt{2}ab)a

4

+b

4

=(a

2

+b

2

+

2

ab)(a

2

+b

2

−

2

ab)

Or

a^4 + b^4 = (a^2 +\sqrt{2}ab+ b^2 )(a^2 -\sqrt{2}ab+ b^2 )a

4

+b

4

=(a

2

+

2

ab+b

2

)(a

2

−

2

ab+b

2

)

Answer 2

Answer:

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