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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
\(a,\left(x-y-4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(3x-2y-5\right)\left(-x-4y-3\right)\)
\(b,\left(2x^2+1\right)^2+6\left(2x^2+1\right)+9\)
\(=\left(2x^2+4\right)^2\)
\(36x^2-\left(3x-2\right)^2\)
\(=\left(6x\right)^2-\left(3x-2\right)^2\)
\(=\left(6x+3x-2\right)\left(6x-3x+2\right)\)
\(=\left(9x-2\right)\left(3x+2\right)\)
\(-49x^2+9\)
\(=3^2-\left(7x\right)^2\)
\(=\left(3-7x\right)\left(3+7x\right)\)
a) 16(4x+5)2 - 25(2x+2)2
\(=\left[4\left(4x+5\right)\right]^2-\left[5\left(2x+2\right)\right]^2\)
\(=\left[4\left(4x+5\right)+5\left(2x+2\right)\right]\left[4\left(4x+5\right)-5\left(2x+2\right)\right]\)
\(=\left(16x+20+10x+10\right)\left(16x+20-10x-10\right)\)
\(=\left(26x+30\right)\left(6x+10\right)\)
\(b,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-2y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-3y+5\right)\)
\(c,\left(x+1\right)^4-\left(x-1\right)^4\)
\(=\left(x+1\right)^{2^2}-\left(x-1\right)^{2^2}\)
\(=\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\)
\(=\left(x^2+2x+1+x^2-2x+1\right)\left[\left(x+1+x-1\right)\left(x+1-x+1\right)\right]\)
\(=\left(2x^2+2\right)2x.2\)
\(=4x.2\left(x^2+1\right)\)
\(=8x\left(x^2+1\right)\)
\(x^4+x^2-2=x^4-x^2+2x^2-2 \)
\(=x^2\left(x^2-1\right)+2\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+2\right)\)
\(=\left(x+1\right)\left(x-1\right)\left(x^2+2\right)\)
1. 2x2 - 18 = 2 • (x2 - 9) = 2 . (x-3).(x+3)
2.x2- 7xy+ 10y2=((x2) - 7xy) + (2•5y2)=(x - 2y)•(x - 5y)
3.16x3y+0.5y2 =((16 • (x3)) • y) + (— • y2) 2= y2 ((16 • (x3)) • y) +\(\dfrac{y^2}{2}\)= (24x3 • y) + \(\dfrac{y^2}{2}\)
= \(\dfrac{\text{24x3y • 2 + y2}}{2}\) =\(\dfrac{\text{32x^3y + y2}}{2}\) = 32x3y + y2 = y • (32x3 + y) = \(\dfrac{\text{y • (32x^3 + y) }}{2}\)
4.x4-4x3+4x2 = ((x4) - (4 • (x3))) + 22x2 =((x4) - 22x3) + 22x2 = x4 - 4x3 + 4x2
= x2 • (x2 - 4x + 4) = x2 • (x - 2)2
5.2ab2-a2b-b3 = (2ab2 - a2b) - b3
= -a2b + 2ab2 - b3 = -b • (a2 - 2ab + b2)
= -b • (a - b)2
Nhớ cho đúng nha
\(a^2-6a+5=\left(a^2-5a\right)-\left(a-5\right)=a\left(a-5\right)-\left(a-5\right)=\left(a-1\right)\left(a-5\right)\)
\(a^2-7a+12=\left(a^2-3a\right)-\left(4a-12\right)=a\left(a-3\right)-4\left(a-3\right)=\left(a-4\right)\left(a-3\right)\)
\(4a^2+4a-3=4a^2-2a+\left(6a-3\right)=2a\left(2a-1\right)+3\left(2a-1\right)=\left(2a+3\right)\left(2a-1\right)\)
X2 - 6x + 5
= x2 - 6x + 5 + 4 - 4
= x2 - 6x + 9 - 22
= ( x - 3 )2 - 22
= ( x - 3 - 2 ) ( x - 3 + 2 )
\(4x^4-9x^2\)
\(=\left(2x^2\right)^2-\left(3x\right)^2\)
\(=\left(2x^2-3x\right)\left(2x^2+3x\right)\)
\(27x^3+125y^3\)
\(=\left(3x\right)^3+\left(5y\right)^3\)
\(=\left(3x+5y\right)\left(9x^2-15xy+25y^2\right)\)
\(16x^2-24xy+9y^2\)
\(=\left(4x\right)^2-2.4x.3y+\left(3y\right)^2\)
\(=\left(4x-3y\right)^2\)