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a2(b + c) + b2(c + a) + c2(a + b) + 2abc
=\(a^2b+a^2c+b^2c+b^2a+ca^2+cb^2+2abc\)
\(=\left(a^2b+ab^2\right)+\left(a^2c+ac^2\right)+\left(b^2c+bc^2\right)+2abc\)
\(=ab\left(a+b\right)+ac\left(a+b\right)+bc\left(a+b\right)+2abc\)
\(=\left(a+b\right)\left(ab+ac+bc+c^2\right)\)
\(=\left(a+b\right)\left(ab+bc\right)+\left(c^2+ac\right)\)
\(=\left(a+b\right)\left(b+c\right)\left(a+c\right)\)
\(\left(x-8\right)^2+36=x^2-16x+64+36=x^2-16x+100>0\)
xem lại đề
dài lắm nên mình làm tắt
1) (x - 5)^2 + (x + 3)^2 = 2(x - 4)(x + 4) - 5x + 7
<=> x^2 - 10x + 25 + x^2 + 6x + 9 = 2x^2 + 8x - 8x - 32 - 5x + 7
<=> 2x^2 - 4x + 34 = 2x^2 - 5x - 25
<=> -4x + 34 = -5x - 25
<=> x + 34 = -25
<=> x = -25 - 34
<=> x = - 59
2) (x + 3)(x - 2) - 2(x + 1)^2 = (x - 3)^2 - 2x^2 + 4x
<=> x^2 - 2x + 3x - 6 - 2x^2 - 4x - 2 = x^2 - 6x + 9 - 2x^2 + 4x
<=> -x^2 - 3x - 8 = -x^2 - 2x + 9
<=> -3x - 8 = -2x + 9
<=> -x - 8 = 9
<=> -x = 9 + 8
<=> x = -17
3) (x + 1)^3 - (x + 2)(x - 4) = (x - 2)(x^2 + 2x + 4) + 2x^2
<=> x^3 + 2x^3 + x + x^2 + 2x + 1 - x^2 + 4x - 2x + 8 = x^3 + 2x^2 + 4x - 2x^2 - 4x - 8 + 2x^2
<=> 2x^2 + 5x + 9 = 2x^2 - 8
<=> 5x + 9 = -8
<=> 5x = -8 - 9
<=> 5x = -17
<=> x = -17/5
4) (x - 2)^3 + (x - 5)(x + 5) = x(x^2 - 5x) - 7x + 3
<=> x^3 - 4x^2 + 4x - 2x^2 + 8x - 8 + x^2 - 5^2 = x^3 - 5x^2 - 7x + 3
<=> 12x - 33 = -7x + 3
<=> 19x - 33 = 3
<=> 19x = 3 + 33
<=> 19x = 36
<=> x = 36/19
5) (x + 4)(x^2 - 4x + 16) - x(x - 4)^2 = 8(x - 3)(x + 3)
<=> x^3 - 4x^2 + 16x + 4x^2 - 16x + 64 - x^3 + 8x^2 - 16x = 8x^2 - 72
<=> -16x + 64 = -72
<=> -16x = -72 - 64
<=> -16x = -136
<=> x = 136/16 = 17/2
6) 4(x - 1)(x + 2) - 5(x + 7) = (2x + 3)^2 - 5x + 3
<=> 4x^2 + 8x - 4x - 8 - 5x - 35 = 4x^2 + 12x + 9 - 5x + 3
<=> -x - 43 = 7x + 12
<=> -8x - 43 = 12
<=> -8x = 12 + 43
<=> -8x = 55
<=> x = -55/8
7) (x - 1)(x^2 + x + 1) + 3(x - 2)^2 = x(x^2 + 3x - 1)
<=> x^3 + x^2 + x - x^2 - x - 1 + 3x^2 - 12x + 12 = x^3 + 3x^2 - x
<=> 3x^2 - 12x + 11 = 3x^2 - x
<=> -12x + 11 = -x
<=> 11 = -x + 12x
<=> 11 = 11x
<=> x = 1
8) (x + 5)(x - 5) - (x + 3)(x^2 - 3x + 9) = 5 - x(x^2 - x - 2)
<=> x^2 - 25 - x^3 + 3x^2 - 9 - 3x^2 + 9x - 27 = 5 - x^3 + x^2 + 2x
<=> -52 - x^3 = 5 - x^3 + 2x
<=> -52 = 5x + 2x
<=> -5x - 2x = 52
<=> -7x = 52
<=> x = -52/7
9) (x + 2)^2 - 2(x + 3)(x - 4) = 5 - x(x - 3)
<=> x^2 + 4x + 4 - 2x^2 + 8x - 6x + 24 = 5 - x^3 + 3x
<=> 6x + 28 = 5 + 3x
<=> 6x + 28 - 3x = 5
<=> 3x + 28 = 5
<=> 3x = 5 - 28
<=> 3x = -23
<=> x = -23/3
10) (x + 7)(x - 7) - (x + 2)^2 = 5(x - 2) + (x - 7)
<=> x^2 - 49 - x^2 - 4x - 4 = 5x - 10 + x - 7
<=> -53 - 4x = 6x - 17
<=> -4x = 6x + 36
<=> -4x - 6x = 36
<=> -10x = 36
<=> x = -36/10 = -18/5
a) \(A=x^2-6x+9-9y^2\)
\(=\left(x-3\right)^2-\left(3y\right)^2\)
\(=\left(x-3-3y\right)\left(x-3+3y\right)\)
b) \(B=x^3-3x^2+3x-1+2\left(x^2-1\right)\)
\(=\left(x-1\right)^3+\left(2x+2\right)\left(x-1\right)\)
\(=\left(x-1\right)\left[\left(x-1\right)^2+2x+2\right]\)
\(=\left(x-1\right).\left(x^2+3\right)\)
a, \(A=\left(x-3\right)^2-9y^2=\left(x-3-3y\right)\left(x-3+3y\right)\)
b, \(B=\left(x-1\right)^3+2\left(x-1\right)\left(x+1\right)=\left(x-1\right)\left[\left(x-1\right)^2+2\left(x+1\right)\right]\)
\(=\left(x-1\right)\left(x^2-2x+1+2x+2\right)=\left(x-1\right)\left(x^2+3\right)\)