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Bài giải:
a) x3 + 127127 = x3 + (1313)3 = (x + 1313)(x2 – x . 1313+ (1313)2)
=(x + 1313)(x2 – 1313x + 1919)
b) (a + b)3 – (a - b)3
= [(a + b) – (a – b)][(a + b)2 + (a + b) . (a – b) + (a – b)2]
= (a + b – a + b)(a2 + 2ab + b2 + a2 – b2 + a2 – 2ab + b2)
= 2b . (3a3 + b2)
c) (a + b)3 + (a – b)3 = [(a + b) + (a – b)][(a + b)2 – (a + b)(a – b) + (a – b)2]
= (a + b + a – b)(a2 + 2ab + b2 – a2 +b2 + a2 – 2ab + b2]
= 2a . (a2 + 3b2)
d) 8x3 + 12x2y + 6xy2 + y3 = (2x)3 + 3 . (2x)2 . y +3 . 2x . y + y3 = (2x + y)3
e) - x3 + 9x2 – 27x + 27 = 27 – 27x + 9x2 – x3 = 33 – 3 . 32 . x + 3 . 3 . x2 – x3 = (3 – x)3
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Bài giải:
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 - 1818 = (2x)3 – (1212)3 = (2x - 1212)[(2x)2 + 2x . 1212 + (1212)2]
= (2x - 1212)(4x2 + x + 1414)
d) 125125x2 – 64y2 = (15x)2(15x)2- (8y)2 = (1515x + 8y)(1515x - 8y)
a) x2 + 6x + 9 = x2 + 2.3x + 32 = (x + 3)2
b) 10x – 25 – x2 = -(x2 -10x + 25) = -(x2 -2.5x + 52)
= -(x – 5)2
c) 8x3 – 1/8= (2x)3 – ( 1/2)3 = (2x – 1/2)[(2x)2 + 2x . 1/2+ (1/2)2]
= (2x – 1/2)(4x2 + x + 1/4)
d) 1/25x2 – 64y2 = (1/5 x)2– (8y)2 = ( 1/5 x + 8y)(1/5x- 8y)
Bài giải:
1.
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 - 1818 = (2x)3 – (1212)3 = (2x - 1212)[(2x)2 + 2x . 1212 + (1212)2]
= (2x - 1212)(4x2 + x + 1414)
d) 125125x2 – 64y2 = (15x)2(15x)2- (8y)2 = (1515x + 8y)(1515x - 8y)
2.
a) x3 + 127127 = x3 + (1313)3 = (x + 1313)(x2 – x . 1313+ (1313)2)
=(x + 1313)(x2 – 1313x + 1919)
b) (a + b)3 – (a - b)3
= [(a + b) – (a – b)][(a + b)2 + (a + b) . (a – b) + (a – b)2]
= (a + b – a + b)(a2 + 2ab + b2 + a2 – b2 + a2 – 2ab + b2)
= 2b . (3a3 + b2)
c) (a + b)3 + (a – b)3 = [(a + b) + (a – b)][(a + b)2 – (a + b)(a – b) + (a – b)2]
= (a + b + a – b)(a2 + 2ab + b2 – a2 +b2 + a2 – 2ab + b2]
= 2a . (a2 + 3b2)
d) 8x3 + 12x2y + 6xy2 + y3 = (2x)3 + 3 . (2x)2 . y +3 . 2x . y + y3 = (2x + y)3
e) - x3 + 9x2 – 27x + 27 = 27 – 27x + 9x2 – x3 = 33 – 3 . 32 . x + 3 . 3 . x2 – x3 = (3 – x)3
a, \(x^3+8=x^3+2x^2-2x^2-4x+4x+8\)
\(=x^2.\left(x+2\right)-2x.\left(x+2\right)+4.\left(x+2\right)\)
\(=\left(x+2\right).\left(x^2-2x+4\right)\)
1)\(8x^6-\frac{1}{125}y^3=\left(2x^2\right)^3-\left(\frac{1}{5}y\right)^3\)
Bạn tự lm tiếp.AD HĐT số (7)
2)\(\left(x+4\right)^3-64=\left(x+4\right)^3-4^3\)
AD HĐT số (7).Tự lm tiếp
3)\(x^6+1=\left(x^2\right)^3+1\)
AD HĐT số (7).Tự lm tiếp
4)\(x^9+1=\left(x^3\right)^3+1\)
AD HĐT số (7).Tự lm tiếp
5,\(x^{12}-y^4=\left(x^6\right)^2-\left(y^2\right)^2\)
AD HĐT số (3).Tự lm tiếp
6)\(x^3+6x^2+12x+8=\left(x+2\right)^3\)
AD HĐT số (4)
7)\(x^3-15x^2+75x-125=\left(x-5\right)^3\)
AD HĐT số (5)
8)\(27a^3-54a^2b+36ab^2-8b^3\)
\(=\left(3a\right)^3-3.\left(3a\right)^2.2b+3.3a.\left(2b\right)^2-\left(2b\right)^3\)
\(=\left(3a-2b\right)^3\)
AD HĐT số (5)
\(27-x^3\)
\(=3^3-x^3\)
\(=\left(3-x\right)\left(9+3x+x^2\right)\)
\(8x^3+0,001\)
\(=\left(2x\right)^3+\left(\dfrac{1}{10}\right)^3\)
\(=\left(2x+\dfrac{1}{10}\right)\left(4x^2-2x\dfrac{1}{10}+\left(\dfrac{1}{10}\right)^2\right)\)
\(=2\left(x+\dfrac{1}{5}\right)\left(4x^2-\dfrac{1}{5}x+\dfrac{1}{100}\right)\)
\(\dfrac{x^3}{125}-\dfrac{y^3}{27}\)
\(=\left(\dfrac{x}{5}\right)^3-\left(\dfrac{y}{3}\right)^3\)
\(=\left(\dfrac{x}{5}-\dfrac{y}{3}\right)\left[\left(\dfrac{x}{5}\right)^2+\dfrac{x}{5}.\dfrac{y}{3}+\left(\dfrac{y}{3}\right)^2\right]\)
\(=\left(\dfrac{x}{5}-\dfrac{y}{3}\right)\left(\dfrac{x^2}{25}+\dfrac{xy}{15}+\dfrac{y^2}{9}\right)\)
b )
Dấu = thứ 3 :
Sửa lại : \(2\left(x+\dfrac{1}{20}\right)\)
a) Ta có : (x - 5)2 - 16
= (x - 5)2 - 42
= (x - 5 - 4)(x - 5 + 4)
= (x - 1)(x - 9)
b) 25 - (3 - x)2
= 52 - (3 - x)2
= (5 - 3 + x)(5 + 3 - x)
= (x + 2)(8 - x)
c) (7x - 4)2 - (2x + 1)2
= (7x - 4 - 2x - 1)(7x - 4 + 2x + 1)
= (5x - 5)(9x - 3)
= 5(x - 1)3(3x - 1)
= 15(x - 1)(3x - 1)
x3 + 7x - 6=x2 . x + 7x - 22 + 2 = (x2 - 22) + (x+7x)+2=(x-2) . (x+2) + 8x + 2
x3 - 5x + 8x - 4=x2 . x -5x + 8x -22 = (x2 - 22) . (x -5x + 8x )=(x-2) . (x+2) . 4x
x3 - 9x2 + 6x + 16=x2 . x - 9x2 + 6x + 16 = (x2 - 9x2) . (x+6x) + 16=(x-9x) . (x+9x) . 7x + 16
k mk nha
a) \(8x^3-\dfrac{1}{27}=\left(2x-\dfrac{1}{3}\right)\left(4x^2+\dfrac{2}{3}x+\dfrac{1}{9}\right)\)
b) \(\dfrac{1}{8}a^3-125b^6=\left(\dfrac{1}{2}a-5b^2\right)\left(\dfrac{1}{4}a+\dfrac{5}{2}ab^2+25b^4\right)\)
c) \(125+\left(a-b\right)^3=\left(5+a-b\right)\left(25-5a+5b+a^2-2ab+b^2\right)\)