Question

计算(2x-1)(2x+1)-2(x^2-2x+1)

分解因式(1).3ab^3-30a^2b^2+75a^3b (2).(3m+2n)^2-4(m-6n)^2 (3).-8ax^2+16axy-8ay^2 (4).(a^2+1)^2-4a^2
已知3^x+2*5^x+2=15^3x-4，求(x-1)^2-3x(x-2)-4的值

Answer 1

(2x-1)(2x+1)-2(x^2-2x+1)

=4x²-1-2x²+4x-2
=2x²+4x-3

分解因式
(1).3ab^3-30a^2b^2+75a^3b
=3ab(b²-10ab+25a²)
=3ab(b-5a)²

(2).(3m+2n)^2-4(m-6n)^2
=(3m+2n+2m-12n)(3m+2n-2m+12n)
=(5m-10n)(m+14n)

(3).-8ax^2+16axy-8ay^2
=-8a(x²-2xy+y²)
=-8a(x-y)²

(4).(a^2+1)^2-4a^2
=(a²+1+2a)(a²+1-2a)
=(a+1)²(a-1)²

已知3^x+2*5^x+2=15^3x-4，求(x-1)^2-3x(x-2)-4的值
3^x+2*5^x+2=15^3x-4

15^x+2=15^3x-4
x+2=3x-4
x=3

(x-1)^2-3x(x-2)-4

=(3-1)²-9(3-2)-4
=4-9-4
=-9

Answer 2

2x^2+4x-3