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(X-y-4)2-(2x+3y-1)2
=(X-Y-4-2X-3Y+1)(X-Y-4+2X+3Y-1)=(-X-4Y-3)(X+2Y-5)
(2x2+1)2+6(2x2+1)+9
=(2X2+1+3)2 (dùng hằng đẳng thức a2 +2ab+b2 =(a+b)2
=(2x2+4)2=(2(x2+2))2=4(x2+2)2
\(a,\left(x-y-4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(3x-2y-5\right)\left(-x-4y-3\right)\)
\(b,\left(2x^2+1\right)^2+6\left(2x^2+1\right)+9\)
\(=\left(2x^2+4\right)^2\)
a) \(x\left(x+4\right)\left(x-4\right)-\left(x^2-1\right)\left(x^2+1\right)\)
\(=x\left(x^2-16\right)-\left(x^4-1\right)\)
\(=x^3-16x-x^4+1\)
bạn ktra lại đề
b) \(x^4+2x^3+5x^2+4x-12\)
\(=x^3\left(x-1\right)+3x^2\left(x-1\right)+8x\left(x-1\right)+12\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+3x^2+8x+12\right)\)
\(=\left(x-1\right)\left[x^2\left(x+2\right)+x\left(x+2\right)+6\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
\(a,\)
\(x^3y-y\)
\(=y\left(x^3-1\right)\)
\(=y\left[\left(x-1\right)\left(x^2+x+1\right)\right]\)
\(=y\left(x-1\right)\left(x^2+x+1\right)\)
\(b,\)
\(x^3y+y\)
\(=y\left(x^3+1\right)\)
\(=y\left[\left(x+1\right)\left(x^2-x+1\right)\right]\)
\(=y\left(x+1\right)\left(x^2-x+1\right)\)
\(c,\)
\(\left(x-y\right)^2-x\left(y-x\right)\)
\(=\left(x-y\right)^2+x\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+x\right)\)
\(=\left(x-y\right)\left(2x-y\right)\)
\(36x^2-\left(3x-2\right)^2\)
\(=\left(6x\right)^2-\left(3x-2\right)^2\)
\(=\left(6x+3x-2\right)\left(6x-3x+2\right)\)
\(=\left(9x-2\right)\left(3x+2\right)\)
\(-49x^2+9\)
\(=3^2-\left(7x\right)^2\)
\(=\left(3-7x\right)\left(3+7x\right)\)
\(\left(x+1\right)^4+\left(x^2+x+1\right)^2\)
\(=2x^4+6x^3+9x^2+6x+2\)(bạn nhân phá ngoặc rồi thu gọn nhé)
\(=\left(2x^4+2x^3+x^2\right)+\left(4x^3+4x^2+2x\right)+\left(4x^2+4x+2\right)\)
\(=x^2\left(2x^2+2x+1\right)+2x\left(2x^2+2x+1\right)+2\left(2x^2+2x+1\right)\)
\(=\left(x^2+2x+2\right)\left(2x^2+2x+1\right)\)
b: \(\left(x^2+4\right)^2-16x^2\)
\(=\left(x^2-4x+4\right)\left(x^2+4x+4\right)\)
\(=\left(x-2\right)^2\cdot\left(x+2\right)^2\)
c: \(x^5-x^4+x^3-x^2\)
\(=x^4\left(x-1\right)+x^2\left(x-1\right)\)
\(=x^2\left(x-1\right)\left(x^2+1\right)\)
Lời giải:
a. Bạn xem lại đề
b. \((x^2+4)^2-16x^2=(x^2+4)^2-(4x)^2=(x^2+4-4x)(x^2+4+4x)\)
\(=(x-2)^2(x+2)^2\)
c.
\(x^5-x^4+x^3-x^2=x^4(x-1)+x^2(x-1)=(x^4+x^2)(x-1)\)
\(=x^2(x^2+1)(x-1)\)
c1.x\(^{^{ }2}\) - x - 6 = x\(^2\) - 3x +2x -6 = x( x- 3 ) + 2( x - 3 ) = ( x - 3)( x +2 )
c2. x\(^2\) - x - 6 = x\(^2\) + 4x + 4 - 5x -10 = ( x + 2)\(^2\) - 5( x + 2 ) = ( x + 2 ) ( x + 2 -5 )
= ( x + 2 )(x - 3 )
tui nghĩ đc có 2 cách này thôi thông cảm