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a) \(=\left(x-2y\right)\left(x^2+5x\right)\)
b) \(=\left(x-1\right)\left(x^2+2x+1\right)=\left(x-1\right)\left(x+1\right)^2\)
c) \(=\left(x^2+1-2x\right)\left(x^2+1+2x\right)\)
\(=\left(x^2-2x+1\right)\left(x^2+2x+1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)^2\)
d) \(=3\left(x+3\right)-\left(x-3\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(3-x+3\right)\)
\(=\left(x+3\right)\left(6-x\right)\)
e) \(=\left(x^2-\frac{1}{3}x\right)\left(x^2+\frac{1}{3}x\right)\)
f) \(=2x\left(x-y\right)-16\left(x-y\right)\)
\(=2\left(x-y\right)\left(x-8\right)\)
a) \(2x\left(x-3\right)^2+5x\left(3-x\right)\)
\(=2x\left(x-3\right)^2-5x\left(x-3\right)\)
\(=\left(x-3\right)\left[2x\left(x-3\right)-5x\right]\)
\(=\left(x-3\right)\left(2x^2-6x-5x\right)\)
\(=\left(x-3\right)\left(2x^2-11x\right)\)
\(=x\left(x-3\right)\left(2x-11\right)\)
b) \(\left(x+3\right)^2-4\left(y^2-2y+1\right)\)
\(=\left(x+3\right)^2-2^2\left(y-1\right)^2\)
\(=\left(x+3\right)^2-\left[2\left(y-1\right)\right]^2\)
\(=\left[\left(x+3\right)-2\left(y-1\right)\right]\left[\left(x+3\right)+2\left(y-1\right)\right]\)
\(=\left(x+3-2y+2\right)\left(x+3+2y-2\right)\)
\(=\left(x-2y+5\right)\left(x+2y+1\right)\)
a) \(2x.\left(x-3\right)^2+5x.\left(-x+3\right)=2x.\left(x-3\right)^2-5x.\left(x-3\right)\)
\(=\left(x-3\right).\left(2x^2-11x\right)=\left(x-3\right).x.\left(2x-11\right)\)
b) \(\left(x+3\right)^2-4.\left(y^2-2y+1\right)=\left(x+3\right)^2-2^2.\left(y-1\right)^2\)
\(=\left(x+3\right)^2-\left[2.\left(y-1\right)\right]^2=\left(x-2y+1\right).\left(x+2y+5\right)\)
1.
a) khong bit bạn xem đề sai k
b) x2 -4x +4 - (x+3)(x-3) = 0
<=> x2 -4x + 4 - x2 +9 = 0
<=> -4x = -13 <=> x= 13/4
c) x2 -3x +2 = 0
<=> x2 -x -2x +2 = 0
<=> x(x-1) - 2( x-1) = 0
<=> (x-1)(x-2) = 0 <=> x = 1 hoặc 2
2.
a) x4 -8 = (x2 -4)(x2 +4) = (x-2)(x+2)(x2 +4)
b)x2 -y2 -2x+2y = (x-y)(x+y) - 2(x-y) = (x-y)(x+y-2)
c)x2 - 5x +6 = x2 -3x -2x +6 = x(x-3) - 2(x-3) = (x-2)(x-3)
a) \(\left(3x-1\right)^2+ \left(x+3\right)^2-5\left(2x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow-15x+55=0\)
\(\Leftrightarrow-15x=0-55\)
\(\Leftrightarrow-15x=-55\)
\(\Leftrightarrow x=\frac{-55}{-15}\)
\(\Rightarrow x=\frac{11}{3}\)
b) \(x^2-4x+4-\left(x+3\right)\left(x-3\right)=0\)
\(\Leftrightarrow x^2-4x-\left(x+3\right)\left(x-3\right)=4-0\)
\(\Leftrightarrow x^2-4x-\left(x+3\right)\left(x-3\right)=4\)
\(\Leftrightarrow4x+9=4\)
\(\Leftrightarrow4x=4+9\)
\(\Leftrightarrow4x=13\)
\(\Rightarrow x=\frac{13}{4}\)
b. x4 - x2 - 2x - 1
=x4-(x2+2x+1)
=x4-(x+1)2
=(x2-x-1)(x2+x+1)
d. ( x2 + 3x + 1 ) ( x2 + 3x - 3 ) - 5
Đặt x2+3x=y
=> (y+1)(y-3)-5=y2-2y-8=(y-1)2-9
=(y-4)(y+2)
=(x2+3x-4)(x2+3x+2)=(x-1)(x+4)(x+1)(x+2)
những bài này dễ lắm bn à, chỉ đơn thuần là áp dụng hđt thui
a) (x+1)(4x-8) =0
x+1=0
x= -1
4x-8 =0
x = 2
b) = 2(x+1)(x+1) = 2(x+1)2
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