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a) \(=x^2+2xy+y^2+x^2-2xy+y^2=2\left(x^2+y^2\right)\)
b) \(=2\left(x^2-y^2\right)+2\left(x^2+y^2\right)=2x^2+2x^2+2y^2-2y^2=4x^2\)( cái này áp dụng luôn kết quả câu trên nha)
c) \(\left(x-y+z\right)^2++2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2=\left(x-y+z+y-z\right)^2=x^2\)
tớ cũng giống Nguyễn Thị Bích Hậu
tích cho nha 1 cái thôi cũng được .
a ) \(\left(x+y\right)^2+\left(x-y\right)^2\)
\(=x^2+2xy+y^2+x^2-2xy+y^2\)
\(=2x^2+2y^2\)
b ) \(2.\left(x-y\right).\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2\)
\(=\left[\left(x-y\right)+\left(x+y\right)\right]\)
\(=2x\)
c tương tự
nguyễn hoàng mai
MÌnh không ghi đề bài đâu .
\(a,=x^2+2xy+y^2+x^2-2xy+x^2=2\left(x^2+y^2\right)\)2)
\(b,=2\left(x^2-y^2\right)+2\left(x^2+y^2\right)=2x^2+2x^2+2y^2-2y^2=4x^2\)( áp dụng kết quả câu trên )
\(c,\left(x-y+z\right)^2+2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2=\left(x-y+z+y-z\right)^2=x^2\)
Lời giải:
Áp dụng các HĐT đáng nhớ:
a)
\(5(x+2)(x-2)-(3-4x)^2=5(x^2-2^2)-(9-24x+16x^2)\)
\(=5x^2-20-9+24x-16x^2\)
\(=-11x^2+24x-29\)
b)
\(2(x-y)(x+y)+(x+y)^2+(x-y)^2\)
\(=2(x^2-y^2)+(x^2+2xy+y^2)+(x^2-2xy+y^2)\)
\(=2x^2-2y^2+2x^2+2y^2=4x^2\)
c)
\((x-y+z)^2+(x-y)^2+2(x-y+z)(y-z)\)
\(=(x-y+z)^2+2(x-y+z)(y-z)+(y-z)^2+(x-y)^2-(y-z)^2\)
\(=(x-y+z+y-z)^2+(x-y)^2-(y-z)^2\)
\(=x^2+(x-y)^2-(y-z)^2=x^2+x^2-2xy+y^2-(y^2-2yz+z^2)\)
\(=2x^2-2xy+2yz-z^2\)
\(A=\left(x-y+z\right)^2+\left(z-y\right)^2+2\left(x-y+z\right)\left(y-z\right)=\left(x-y+z\right)\left[\left(x-y+z\right)+2\left(y-z\right)\right]+\left(z-y\right)^2=\left(x-y+z\right)\left[x+y-z\right]+\left(z-y\right)^2\)\(A=x^2-\left(y-z\right)^2+\left(z-y\right)^2=x^2\)
Câu 1: Rút gọn
a. (x+y)2 + (x-y)2
=x2+2xy+y2+x2-2xy+y2=2x2+2y2
b. 2.(x-y) . (x+y) + (x+y)2 + (x-y)2
=2.(x2-y2)+2x2+2y2=4x2
c. (x-y+z)2 + (z-y)2 +2.(x-y+z) . (z-y)
=x2+y2+z2-2xy-2yz+2zx+z2-2yz+y2+2.(xz-xy-yz+y2+z2-zy)
=x2+2y2+2z2-2xy+2zx-4yz+2xz-2xy-4yz+2y2+2z2
=x2+4y2+4z2-4xy-8yz+4xz
Câu 2: Chứng minh
(ac+bd)2 + (ad-bc)2=a2c2+2abcd+b2d2+a2d2-2abcd+b2c2= a2c2+b2d2+a2d2+b2c2 =(a2+b2) . (c2+d2)
Câu 1:
a. \(\left(x+y\right)^2+\left(x-y\right)^2\)
\(=x^2+2xy+y^2+x^2-2xy+y^2\)
\(=2\left(x^2+y^2\right)\)
b. \(2\left(x-y\right)\left(x+y\right)+\left(x+y^2\right)+\left(x-y\right)^2\)
\(=\left(x+y\right)^2+2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x+y+x-y\right)^2\)
\(=\left(2x\right)^2\)
\(=4x^2\)
\(\left(a\right):\left(x+y\right)^2-\left(x-y\right)^2=x^2+2xy+y^2-\left(x^2-2xy+y^2\right)\\ =x^2+2xy+y^2-x^2+2xy-y^2\\ =4xy\)
\(\left(b\right):\left(x-y-z\right)^2+\left(x+y+z\right)^2\\ =\left[\left(x-y\right)-z\right]^2+\left[\left(x+y\right)+z\right]^2\\ =\left(x-y\right)^2-2z\left(x-y\right)+z^2+\left(x+y\right)^2+2z\left(x+y\right)+z^2\\ =x^2-2xy+y^2-2xz+2yz+z^2+x^2+2xy+y^2+2xz+2yz+z^2\\ =2x^2+2y^2+2z^2+4yz\)
\(\left(c\right):\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\\ =\left[\left(x+y\right)-\left(x-y\right)\right]^2\\ =\left(x+y-x+y\right)^2\\ =\left(2y\right)^2=4y^2\)