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1: =(16x^2-8x+1)-y^2
=(4x-1)^2-y^2
=(4x-1-y)(4x-1+y)
2: =(x^2-2xy+y^2)-z^2
=(x-y)^2-z^2
=(x-y-z)(x-y+z)
3: =(x^2+4xy+4y^2)-16
=(x+2y)^2-4^2
=(x+2y-4)(x+2y+4)
4: =(x^2-4xy+4y^2)-16
=(x-2y)^2-4^2
=(x-2y-4)(x-2y+4)
a,x2-8x+16=(x-4)2
b,(x-5y)(x+5y)=x2-25y2
c,4x4-16=4(x2-2)(x2+2)
d,x2+4xy+4y2=(x+2y)2
b) \(x^2-4y^2-2x+4y\)
\(=\left(x^2-4y^2\right)-\left(2x-4y\right)\)
\(=\left[x^2-\left(2y\right)^2\right]-\left(2x-4y\right)\)
\(=\left(x-2y\right).\left(x+2y\right)-2.\left(x-2y\right)\)
\(=\left(x-2y\right).\left(x+2y-2\right)\)
c) \(x^3-25x\)
\(=x.\left(x^2-25\right)\)
\(=x.\left(x^2-5^2\right)\)
\(=x.\left(x-5\right).\left(x+5\right)\)
d) \(x^4+64\)
\(=\left(x^2\right)^2+16x^2+64-16x^2\)
\(=\left[\left(x^2\right)^2+16x^2+64\right]-16x^2\)
\(=\left[\left(x^2\right)^2+2.x^2.8+8^2\right]-16x^2\)
\(=\left(x^2+8\right)^2-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2+8-4x\right).\left(x^2+8+4x\right)\)
g) \(3x^2-8x+5\)
\(=3x^2-5x-3x+5\)
\(=\left(3x^2-3x\right)-\left(5x-5\right)\)
\(=3x.\left(x-1\right)-5.\left(x-1\right)\)
\(=\left(x-1\right).\left(3x-5\right)\)
Chúc bạn học tốt!
a: \(\Leftrightarrow x^2-2x+1+y^2+4y+4=0\)
=>(x-1)^2+(y+2)^2=0
=>x=1 và y=-2
b: \(\Leftrightarrow2x^2+2y^2-16x+32+16y+32=0\)
\(\Leftrightarrow2\left(y-4\right)^2+2\left(x+4\right)^2=0\)
=>y=4; x=-4
a. 2x-1-x2= -(x2-2x+1)=-(x-1)2
b. 8x3+y6=(2x)3+(y2)3
=(2x+y2)(4x2-2xy2+y4)
c. x2-16+4xy+4y2=(x2+4xy+4y2)-16
=(x+2y)2-16=(x+2y+4)(x+2y-4)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
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