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a: ta có: \(x\left(x-y\right)+y\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y\right)\)
\(=x^2-y^2\)
b: Ta có: \(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
\(=x^n+x^{n-1}\cdot y-x^{n-1}\cdot y-y^n\)
\(=x^n-y^n\)
![](https://rs.olm.vn/images/avt/0.png?1311)
x(x – y) + y(x – y)
= x.x – x.y + y.x – y.y
= x2 – xy + xy – y2
= x2 – y2 + (xy – xy)
= x2 – y2
![](https://rs.olm.vn/images/avt/0.png?1311)
a) x(x – y) + y(x – y) = x2 – xy + yx – y2 = x2 – xy + xy – y2 = x2 – y2
b) xn–1(x + y) – y( xn–1 + yn–1 ) = xn + xn–1y – yxn–1 – yn
= xn + xn–1y – xn–1y – yn = xn - yn
a) x (x - y) + y (x - y) = x2 – xy+ yx – y2
= x2 – xy+ xy – y2
= x2 – y2
b) xn – 1 (x + y) – y(xn – 1 + yn – 1) =xn+ xn – 1y – yxn – 1 - yn
= xn + xn – 1y - xn – 1y - yn
= xn – yn.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
=\(x^n+x^{n-1}y-x^{n-1}y-y^n\)
=\(x^n-y^n\)
\(x\left(x-y\right)+y\left(x-y\right)\)
\(=x.x-x.y+y.x-y.y\)
\(=x^2-xy+yx-y^2\)
=\(x^2-y^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
xn - 1(x + y) - y(xn - 1 + yn - 1)
= xn - x + y - yxn - y2 n - 1
![](https://rs.olm.vn/images/avt/0.png?1311)
1. \(x\left(x-y\right)+y\left(x+y\right)=x^2+y^2\)
Thay x = - 6, y = 8 ta suy ra \(x^2+y^2=\left(-6\right)^2+8^2=100\)
2. \(x\left(x^2-y\right)-x^2\left(x+y\right)+y\left(x^2-y\right)=x^3-xy-x^3-x^2y+x^2y-y^2\)
\(-xy-y^2=-\frac{1}{2}.\left(-100\right)-\left(-100\right)^2\)
\(=50-10000=-9950\)
1) Khi x = -6 y = 8 thì x(x - y) + y(x + y) = -6(-6 - 8) + 8(-6 + 8)
= 84 + 16 = 110
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\(P=\left(x-y\right)^2+\left(x+y\right)^2-2\left(x-y\right)\left(x+y\right)-4x^2\\ P=\left(x-y-x-y\right)^2-4x^2\\ P=4y^2-4x^2=4\left(y-x\right)\left(x+y\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1) x(x-y)+y(x-y)
=(x-y)(x+y) (đặt nhân tử chung)
=x^2-y^2 (hằng đẳng thức số 3)
1. \(x\left(x-y\right)+y\left(x-y\right)=\left(x-y\right)\left(x+y\right)=x^2-y^2\)
\(2.x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
\(=x^n+y.x^{n-1}-y.x^{n-1}-y^n=x^n-y^n\)