Rút gọn biểu thức ( làm đầy đủ nha )
a, (x + y)^2 + (x – y)^2
b, 2(x – y)(x + y) + (x + y)^2 + (x – y)^2
c, (x – y + z)^2 + (z – y)^2 + 2(x – y + z)(y – z)
Rút gọn biểu thức ( làm đầy đủ nha ) a, (x + y)^2 + (x – y)^2 b, 2(x – y)(x + y) + (x + y)^2 + (x – y)^2 c, (x – y + z)^2 + (z – y)^2 + 2(x – y + z)(y
By Samantha
Đáp án:
Giải thích các bước giải:
a, `(x + y)^2 + (x – y)^2`
`= x^2+2xy+y^2+x^2-2xy+y^2`
`=2x^2+2y^2`
b) `2(x – y)(x + y) + (x + y)^2 + (x – y)^2`
`=2(x^2-y^2)+x^2+2xy+y^2+x^2-2xy+y^2`
`=2x^2-2y^2+x^2+2xy+y^2+x^2-2xy+y^2`
`=4x^2`
c) `(x – y + z)^2 + (z – y)^2 + 2(x – y + z)(y – z)`
\(=\left(x-y+z\right)^2+\left(z-y\right)^2+\left(x-y+z\right)\left(y-z\right)+\left(x-y+z\right)\left(y-z\right)\)
\(=\left(x-y+z\right)^2+\left(x-y+z\right)\left(y-z\right)+\left(z-y\right)^2+\left(x-y+z\right)\left(y-z\right)\)
\(=\left(x-y+z\right)^2+\left(x-y+z\right)\left(y-z\right)+\left(z-y\right)^2-\left(x-y+z\right)\left(z-y\right)\)
\(=\left(x-y+z\right)\left(x-y+y+z-z\right)+\left(z-y\right)[z-y-\left(x-y+z\right)]\)
\(=\left(x-y+z\right)x+\left(z-y\right)\left(z-y-x+y-z\right)\)
\(=x^2-xy+xz+\left(z-y\right)\left(-x\right)\)
\(=x^2-xy+xz-xz+xy\)
\(=x^2\)
Đáp án:
Giải thích các bước giải:
\(a,\ (x+y)^{2}+(x-y)^{2}\\ =x^{2}+2xy+y^{2}+x^{2}-2xy+y^{2}\\ =(x^{2}+x^{2})+(2xy-2xy)+(y^{2}+y^{2})\\ =2x^{2}+2y^{2}\\ b,\ 2(x-y)(x+y)+(x+y)^{2}+(x-y)^{2}\\ =(x+y)^{2}+2(x+y)(x-y)+(x-y)^{2}\\ =(x+y+x-y)^{2}\\ =\left [(x+x)+(y-y) \right ]^{2}\\ =(2x)^{2}\\ =4x^{2}\\ c,\ (x-y+z)^{2}+(z-y)^{2}+2(x-y+z)(y-z)\\ =(x-y+z)^{2}-2(x-y+z)(z-y)+(z-y)^{2}\\ =(x-y+z-z+y)^{2}\\ =\left [x+(-y+y)+(z-z) \right ]^{2}\\ =x^{2}\)
chúc bạn học tốt!