Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(=x\left(x^2-6x+9-y^2\right)\)
\(=x\left(x-3-y\right)\left(x-3+y\right)\)
a) Xem lại đề
b) x³ - 4x²y + 4xy² - 9x
= x(x² - 4xy + 4y² - 9)
= x[(x² - 4xy + 4y² - 3²]
= x[(x - 2y)² - 3²]
= x(x - 2y - 3)(x - 2y + 3)
c) x³ - y³ + x - y
= (x³ - y³) + (x - y)
= (x - y)(x² + xy + y²) + (x - y)
= (x - y)(x² + xy + y² + 1)
d) 4x² - 4xy + 2x - y + y²
= (4x² - 4xy + y²) + (2x - y)
= (2x - y)² + (2x - y)
= (2x - y)(2x - y + 1)
e) 9x² - 3x + 2y - 4y²
= (9x² - 4y²) - (3x - 2y)
= (3x - 2y)(3x + 2y) - (3x - 2y)
= (3x - 2y)(3x + 2y - 1)
f) 3x² - 6xy + 3y² - 5x + 5y
= (3x² - 6xy + 3y²) - (5x - 5y)
= 3(x² - 2xy + y²) - 5(x - y)
= 3(x - y)² - 5(x - y)
= (x - y)[(3(x - y) - 5]
= (x - y)(3x - 3y - 5)
1: \(\left(x-2\right)^2-4x+8\)
\(=\left(x-2\right)\left(x-2-4\right)\)
\(=\left(x-2\right)\left(x-6\right)\)
3: \(a^3+6a^2+9a-ab^2\)
\(=a\left(a^2+6a+9-b^2\right)\)
\(=a\left(a+3-b\right)\left(a+3+b\right)\)
\(2x^2-xy+9x-3y+4=0\)
\(\Rightarrow-y\left(x+3\right)+x\left(2x+9\right)=-4\)
\(\Rightarrow-y\left(x+3\right)=-4-x\left(2x+9\right)\)
\(\Rightarrow y=\dfrac{x\left(2x+9\right)+4}{x+3}=\dfrac{2x^2+9x+4}{x+3}\)
-Vì x,y nguyên nên:
\(\left(2x^2+9x+4\right)⋮\left(x+3\right)\)
\(\Rightarrow\left(2x^2+6x+3x+9-5\right)⋮\left(x+3\right)\)
\(\Rightarrow\left[2x\left(x+3\right)+3\left(x+3\right)-5\right]⋮\left(x+3\right)\)
\(\Rightarrow5⋮\left(x+3\right)\)
\(\Rightarrow x+3\in\left\{1;5;-1;-5\right\}\)
\(\Rightarrow x\in\left\{-2;2;-4;-8\right\}\)
*\(x=-2\Rightarrow y=\dfrac{2.\left(-2\right)^2+9.\left(-2\right)+4}{-2+3}=-6\)
\(x=2\Rightarrow y=\dfrac{2.2^2+9.2+4}{2+3}=6\)
\(x=-4\Rightarrow y=\dfrac{2.\left(-4\right)^2+9.\left(-4\right)+4}{-4+3}=0\)
\(x=-8\Rightarrow y=\dfrac{2.\left(-8\right)^2+9.\left(-8\right)+4}{-8+3}=-12\)
-Vậy các cặp số \(\left(x,y\right)\) là \(\left(-2,-6\right);\left(2,6\right);\left(-4,0\right);\left(-8;-12\right)\)
\(x^3+6x^2+9x-xy^2\)
\(=x\left(x^2+6x+9-y^2\right)\)
\(=x\left[\left(x+3\right)^2-y^2\right]\)
\(=x\left(x+3-y\right)\left(x+3+y\right)\)