中二指數和因式分解的問題~!(10點)

指數:
1)
若果是 2^(y+1)+[2^(y+2)]/9
={9*[2^(y+1)]+[2^(y+2)]}/9
={9*[2^(y+1)]+2*[2^(y+1)]}/9
=(11/9)*[2^(y+1)] 2)
[5^(3y)]/[25^y]-[5^(2y-1)]
=[5^(3y)]/[(5^2)^y]-[5^(2y-1)]
=[5^(3y)]/[5^(2y)]-[5^(2y-1)]
=[5^(3y-2y)]-[5^(2y-1)]
=(5^y)-[5^(2y-1)]
=(5^y){1-[5^(y-1)]}
=(5^y){[5-(5^y)]/5}
=[5^(y-1)][5-(5^y)] 3)
[3^(-2)] X [27^(y+1)]/[9^(-2y)]
=[3^(-2)] X [(3^3)^(y+1)]/[(3^2)^(-2y)]
=[3^(-2)] X {3^[3(y+1)]}/{3^[2(-2y)]}
=[3^(-2)] X [3^(3y+3)]/[3^(-4y)]
=3^[(-2)+(3y+3)-(-4y)]
=3^(-2+3y+3+4y)
=3^(7y+1) 4)
[6^(2y)]/[4^y] X (3^2)
=[(2X3)^(2y)]/[(2^2)^y] X (3^2)
=[2^(2y)]X[3^(2y)]/[(2^(2y)] X (3^2)
=[3^(2y)] X (3^2)
=3^(2y+2) 因式分解:
1)
20x^2+44xy-15y^2
=(10x-3y)(2x+5y) 2)
-6x^2+46xy-60y^2
=(3x-5y)(-2x+12y) 3)
若果是 (2a+b)(2a-b)-4a^2+1
=(2a)^2-b^2-4a^2+1
=4a^2-b^2-4a^2+1
=1-b^2
=1^2-b^2
=(1-b)(1+b)
4)
a^3+b^3-(a^2)b-a(b^2)
=(a+b)(a^2-ab+b^2)-(a^2)b-a(b^2)
=(a+b)(a^2-ab+b^2)-ab(a+b)
=(a+b)(a^2-ab+b^2-ab)
=(a+b)(a^2-2ab+b^2)
=(a+b)[(a-b)^2]

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