Giúp mình với
a, x^(2)+y^(2)=(x+y)^(2)-2xy
b, (a+b)^2-(a-b)(a+b)=2b(a+b)
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14 tháng 8 2023
a: =x^2+2xy+y^2-4x^2y^2
=(x+y)^2-(2xy)^2
=(x+y+2xy)(x+y-2xy)
b: =49-(a^2-2ab+b^2)
=49-(a-b)^2
=(7-a+b)(7+a-b)
c: =\(a^2-\left(b^2-4bc+4c^2\right)\)
\(=a^2-\left(b-2c\right)^2=\left(a-b+2c\right)\left(a+b-2c\right)\)
d:
\(=\left(bc\right)^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(bc-b^2-c^2+a^2\right)\left(bc+b^2+c^2-a^2\right)\)
e: \(=\left(a+b\right)^2+2c\left(a+b\right)+c^2+\left(a+b\right)^2-2c\left(a+b\right)+c^2-4c^2\)
=2(a+b)^2-2c^2
=2[(a+b)^2-c^2]
=2(a+b-c)(a+b+c)
28 tháng 6 2023
A+(2x^2-y^5)=5x^2-3x^2+2xy
=>A+2x^2-y^5=2x^2+2xy
=>A=2xy+y^5
B-(3xy+x^2-2y^2)=4x^2-xy+y^2
=>B=4x^2-xy+y^2+3xy+x^2-2y^2
=>B=5x^2+2xy-y^2
NC
22 tháng 8 2020
Bài 1:
a) \(\left(x+y\right)^2-y^2=x^2+2xy+y^2-y^2=x^2+2xy=x\left(x+2y\right)\)
b) Sửa đề: \(\left(x^2+y^2\right)^2-\left(2xy\right)^2=\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\)
\(=\left(x-y\right)^2\left(x+y\right)^2\)
c) \(x\left(x-3y\right)^2+y\left(y-3x\right)^2=x\left(x^2-6xy+9y^2\right)+y\left(y^2-6xy+9x^2\right)\)
\(=x^3-6x^2y+9xy^2+y^3-6xy^2+9x^2y\)
\(=x^3+3x^2y+3xy^2+y^3=\left(x+y\right)^3\)
NC
22 tháng 8 2020
Bài 2:
a) \(\left(a+b\right)^3+\left(a-b\right)^3=\left(a+b+a-b\right)\left[\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
\(=2a\left(a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2\right)\)
\(=2a\left(a^2+3b^2\right)\)
b) \(\left(a+b\right)^3-\left(a-b\right)^3=\left(a+b-a+b\right)\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
\(=2b\left(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right)\)
\(=2b\left(b^2+3a^2\right)\)
BH
4 tháng 10 2016
a)\(a^4+a^3+a^3b+a^2b=\left(a^4+a^3b\right)+\left(a^3+a^2b\right)\)
\(=a^3\left(a+b\right)+a^2\left(a+b\right)\)
\(=\left(a^3+a^2\right)\left(a+b\right)\)
\(=a^2\left(a+1\right)\left(a+b\right)\)
b)\(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left[\left(x-y+4\right)-\left(2x+3y-1\right)\right]\left[\left(x-y+4\right)+\left(2x+3y-1\right)\right]\)
\(=\left(x-y+4-2x-3y+1\right)\left(x-y+4+2x+3y-1\right)\)
\(=\left(-x-4y+5\right)\left(4x+2y+3\right)\)
c)\(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)
\(=x^2\left(y-z\right)+y^2\left(z-y+y-x\right)+z^2\left(x-y\right)\)
\(=x^2\left(y-z\right)-y^2\left(y-z\right)-y^2\left(x-y\right)+z^2\left(x-y\right)\)
\(=\left(y-z\right)\left(x^2-y^2\right)-\left(x-y\right)\left(y^2-z^2\right)\)
\(=\left(y-z\right)\left(x-y\right)\left(x+y\right)-\left(x-y\right)\left(y-z\right)\left(y+z\right)\)
\(=\left(y-z\right)\left(x-y\right)\left(x+y-y-z\right)\)
\(=\left(y-z\right)\left(x-y\right)\left(x-z\right)\)
\(a,\left(x+y\right)^2-2xy=x^2+2xy+y^2-2xy=x^2+y^2\left(đpcm\right)\\ b,\left(a+b\right)^2-\left(a-b\right)\left(a+b\right)=\left(a+b\right)\left(a+b-a+b\right)=2b\left(a+b\right)\left(đpcm\right)\)
Ô CMR à :v