simplify (2a²+5b) ²+(2a²-5b)²
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Answer: 8a⁴+50b⁴
Step-by-step explanation:
x²+y²=(x+y)²-2xy
x=2a²+5b², y=2a²-5b²
(2a²+5b²)+(2a²-5b²)=
=(2a²+5b²+2a²-5b²)²-2(2a²+5b² )(2a²-5b²)=
=(4a²)²-2(2a²+5b² )(2a²-5b²)
(x+y)(x-y)=x²-y²
(4a²)²-2((2a²)²-(5b²)²)=16a⁴-2(4a⁴-25b⁴)=16a⁴-8a⁴+50b⁴=
=8a⁴+50b⁴
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