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x^2(1-x^2)-4-4x^2
=x^2-x^4-4-4x^2
=x^2-(x^2+1)^2
=(x-x^2-1)(x+x^2+1)
Rút gọn thôi chứ phân tích sao được ._.
( x - 3 )2 - ( 4x + 5 )2 - 9( x + 1 )2 - 6( x - 3 )( x + 1 )
= x2 - 6x + 9 - ( 16x2 + 40x + 25 ) - 9( x2 + 2x + 1 ) - 6( x2 - 2x - 3 )
= x2 - 6x + 9 - 16x2 - 40x - 25 - 9x2 - 18x - 9 - 6x2 + 12x + 18
= -30x2 - 52x - 7
Sửa đề lại 1 chút là phân tích được mà bn Quỳnh:))
Ta có: \(\left(x-3\right)^2-\left(4x+5\right)^2+9\left(x+1\right)^2-6\left(x-3\right)\left(x+1\right)\)
\(=\left[\left(x-3\right)^2-6\left(x-3\right)\left(x+1\right)+9\left(x+1\right)^2\right]-\left(4x+5\right)^2\)
\(=\left(x-3-9x-9\right)^2-\left(4x+5\right)^2\)
\(=\left(8x+12\right)^2-\left(4x+5\right)^2\)
\(=\left(4x+7\right)\left(12x+17\right)\)
\(A=\left(1+x^2\right)^2-4x\left(1-x^2\right)\)
\(=x^4+2x^2+1-4x+4x^3\)
\(=x^4+4x^3+2x^2-4x+1\)
\(=\left(x^4+2x^3-x^2\right)+\left(2x^3+4x^2-2x\right)-\left(x^2+2x-1\right)\)
\(=\left(x^2+2x-1\right)^2\)
( 1 + x2)2 - 4x ( 1 - x2 )
= x4 + 2x2 + 1 - 4x + 4x3
= x3 + 2x2 - x + 2x3 + 4x2 - 2x - x2 - 2x + 1
= x ( x2 + 2x - 1 ) + 2x ( x2 + 2x - 1 ) - ( x2 + 2x - 1 )
= ( x2 + 2x - 1 ) ( x2 + 2x - 1 )
= ( x2 + 2x - 1)2
a) Đặt: x = a- b; y = b - c ; z = c- a
Ta có: x + y + z = 0
=> \(A=x^3+y^3+z^3=3xyz+\left(x+y+z\right)\left(x^2+y^2+z^2-xy-xz-yz\right)=3xyz\)
=> \(A=3xyz=3\left(a-b\right)\left(b-c\right)\left(c-a\right)\)
b) Đặt: \(a=x^2-2x\)
Ta có: \(B=a\left(a-1\right)-6=a^2-a-6=\left(a+2\right)\left(a-3\right)=\left(x^2-2x+2\right)\left(x^2-2x-3\right)\)
\(=\left(x^2-2x+2\right)\left(x+1\right)\left(x-3\right)\)
d) \(D=4\left(x^2+2x-8\right)\left(x^2+7x-8\right)+25x^2\)
Đặt: \(x^2-8=t\)
Ta có: \(D=4\left(t+2x\right)\left(t+7x\right)+25x^2\)
\(=4t^2+36xt+81x^2=\left(2t+9x\right)^2\)
\(=\left(2x^2+9x-16\right)^2\)
(1+x2)2−4x(1−x2)
= \(-\left(1-x^2\right)^2-4x\left(1-x^2\right)\)
đặt \(\left(1-x^2\right)\)= a
ta có :
- a . a - 4x .a
= a ( - a - 4x )
thay a = \(\left(1+x^2\right)\) ta có
\(\left(1+x^2\right)\left(1-x^2-4x\right)\)
phân tích tiếp nhé !
\(\left(1+x^2\right)^2-4x\left(1-x^2\right)\)
\(=x^4+4x^3+2x^2-4x+1\)
\(=\left(x^4+2x^3-x^2\right)+\left(2x^3+4x^2-2x\right)-\left(x^2+2x-1\right)\)
\(=x^2\left(x^2+2x-1\right)+2x\left(x^2+2x-1\right)-\left(x^2+2x-1\right)\)
\(=\left(x^2+2x-1\right)^2\)