已知2的x次方=a,2的y次方=b,求2的x+y的次方+2的3x+2y次方

题目

已知2的x次方=a,2的y次方=b,求2的x+y的次方+2的3x+2y次方

答案

2^(x+y)+2^(3x+2y)
=2^x×2^y+2^3x×2^2y
=2^x×2^y+(2^x)³×(2^y)²,把2^x=a,2^y=b代入
=a×b+a³×b²
=ab+a³b²