Question

Find the value of (a⁴-b⁴), given that (a²+b²) = 130, (a-b) = 2 and (a+b) 16.​

Answer 1

Answer:

4160

Step-by-step explanation:

$a^{4} -b^{2} \\(a^{2} )^{2} -(b^{2} )^{2} \\(a^{2} +b^{2} )(a^{2} -b^{2} )\\(130)(16)(2)\\(130)(32)\\4160$

Answer 2

(a⁴-b⁴)

$= (a {}^{2} + b {}^{2} )(a {}^{2} - b {}^{2}) \\ = (a {}^{2} + b {}^{2} )( \: (a + b)(a - b) \: ) \\ = (130) \: ( \: (16)(2) \: ) \\ = (130)(30 ) \\ = 390$