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a) \(12x-9-4x^2\)
\(=-\left(4x^2-12x+9\right)\)
\(=-\left(2x-3\right)^2\)
b)\(1-9x+27x^2-27x^3\)
\(=\left(1-3x\right)^{^3}\)
c)\(\frac{x^2}{4}+2xy+4y^2-25\)
\(=\left(\frac{x}{2}+2y\right)^2-5^2\)
\(=\left(\frac{x}{2}+2y-5\right)\left(\frac{x}{2}+2y+5\right)\)
d)\(\left(x^2-4x\right)^2-8\left(x^2-4x\right)+15\)
\(=\left(x^2-4x\right)^2-3\left(x^2-4x\right)-5\left(x^2-4x\right)+15\)
\(=\left(x^2-4x\right)\left(x^2-4x-3\right)-5\left(x^2-4x-3\right)\)
\(=\left(x^2-4x-5\right)\left(x^2-4x-3\right)\)
\(=\left(x^2+x-5x-5\right)\left(x^2-4x-3\right)\)
\(=\left[x\left(x+1\right)-5\left(x+1\right)\right]\left(x^2-4x-3\right)\)
\(=\left(x-5\right)\left(x+1\right)\left(x^2-4x-3\right)\)
Chúc bạn học tốt !
\(\frac{2}{5}x\left(y-1\right)-\frac{2}{5}y\left(y-1\right)\)
\(=\left(y-1\right)\left[\left(\frac{2}{5}x-\frac{2}{5}y\right)\right]\)
\(=\left(y-1\right)\frac{2}{5}\left(x-y\right)\)
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
WOW !!! Tốc độ đánh máy của bạn thần thánh thật đấy......2 phút mà nhiều quá trời luôn
d
\(x^4+2x^3-4x-4\)
\(=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)
\(=\left(x^2+x\right)^2-\left(x+2\right)^2\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
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)
Bài 1 :
a ) \(2x\left(x+1\right)+2\left(x+1\right)=\left(x+1\right)\left(2x+2\right)=2\left(x+1\right)^2\)
b ) \(y^2\left(x^2+y\right)-zx^2-zy=y^2\left(x^2+y\right)-z\left(x^2+y\right)=\left(x^2+y\right)\left(y^2-z\right)\)
c ) \(4x\left(x-2y\right)+8y\left(2y-x\right)=4x\left(x-2y\right)-8y\left(x-2y\right)=4\left(x-2y\right)^2\)
d ) \(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)=\left(x+1\right)\left(3x^2+3x-5x^2+7\right)=\left(x+1\right)\left(3x-2x^2+7\right)\)
e ) \(x^2-6xy+9y^2=\left(x-3x\right)^2\)
Bài 1 :
f ) \(x^3+6x^2y+12xy^2+8y^3=\left(x+2y\right)^3\)
g ) \(x^3-64=\left(x-4\right)\left(x^2+4x+16\right)\)
h ) \(125x^3+y^6=\left(5x+y^2\right)\left(25x^2-5xy^2+y^4\right)\)
Bạn tách ra thành các dòng để bọn mình dễ nhìn hơn nhé.
a:Sửa đề: \(\left(2x+5\right)^2-\left(x-3\right)^2\)
=(2x+5-x+3)(2x+5+x-3)
=(x+8)(3x+2)
b:Sửa đề: \(25\left(2x-1\right)^2-9\left(x+1\right)^2\)
\(=\left(10x-5\right)^2-\left(3x+3\right)^2\)
=(10x-5-3x-3)(10x-5+3x+3)
=(7x-8)(13x-2)
c: \(1-9x+27x^2-27x^3\)
\(=1^3-3\cdot1^2\cdot3x+3\cdot1\cdot\left(3x\right)^2-\left(3x\right)^3\)
\(=\left(1-3x\right)^3\)
d: \(49-a^2+2ab-b^2\)
\(=7^2-\left(a-b\right)^2\)
=(7-a+b)(7+a-b)
e: \(-4x^2-12xy-9y^2+25\)
\(=25-\left(4x^2+12xy+9y^2\right)\)
\(=5^2-\left(2x+3y\right)^2\)
=(5-2x-3y)(5+2x+3y)