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Bài 1:
a) Biến đổi vế trái ta được:
\(\left(a+b\right)^2+\left(a-b\right)^2=a^2+2ab+b^2+a^2-2ab+b^2=2a^2+2b^2=VP\)
=>đpcm
b) Biến đổi vế trái ta có:
\(\left(a+b+c\right)^2+a^2+b^2+c^2\)
\(=a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2\)
\(=\left(a^2+2ab+b^2\right)+\left(b^2+2bc+c^2\right)+\left(c^2+2ca+a^2\right)\)
\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(c+a\right)^2=VP\)
=>đpcm
Bài 1:
a: \(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
b: \(=xy\left(x-y\right)-\left(x-y\right)=\left(x-y\right)\left(xy-1\right)\)
c: \(=x\left(x^2+2x+1\right)=x\left(x+1\right)^2\)
d: \(=x\left(x+y\right)+\left(x+y\right)\left(x-y\right)=\left(x+y\right)\left(2x-y\right)\)
e: \(=5xy\left(x-2y^2\right)\)
g: \(=\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+6\right)\left(x+2\right)\left(x-1\right)\)
h: \(=\left(x+2y\right)^2-16=\left(x+2y+4\right)\left(x+2y-4\right)\)
k: \(=2x^2-8x+3x-12=\left(x-4\right)\left(2x+3\right)\)
c: \(5\left(a+b\right)+x\left(a+b\right)\)
=(a+b)(x+5)
d: \(\left(a-b\right)^2-\left(b-a\right)\)
\(=\left(a-b\right)^2+\left(a-b\right)\)
=(a-b)(a-b+1)
e: \(=\left(12x^2+6x\right)\left(y+z+y-z\right)\)
\(=2y\cdot6x\cdot\left(2x+1\right)=12xy\left(2x+1\right)\)
a) \(=\left(x-5\right)\left(2+x+5-2x-1\right)=\left(x-5\right)\left(6-x\right)\)
e) \(=\left(ab^3c^2-a^2b^2c^2\right)+\left(ab^2c^3-a^2bc^3\right)=ab^2c^2\left(b-a\right)+abc^3\left(b-a\right)=abc^2\left(b-a\right)\left(b+c\right)\)
Bài 1:
a) \(\left(a-b^2\right)\left(a+b^2\right)=a^2-b^4\)
b) \(\left(a^2+2a-3\right)\left(a^2+2a+3\right)=\left(a^2+2a\right)^2-9\)
c) \(\left(a^2+2a+3\right)\left(a^2-2a-3\right)=a^2-\left(2a+3\right)^2\)
d) \(\left(a^2-2a+3\right)\left(a^2+2a+3\right)=9-\left(a^2-2a\right)^2\)
e) \(\left(-a^2-2a+3\right)\left(-a^2-2a+3\right)=\left(-a^2-2a+3\right)^2\)
g) \(\left(a^2+2a+3\right)\left(a^2-2a+3\right)=\left(a^2+3\right)^2-4a^2\)
f) \(\left(a^2+2a\right)\left(2a-a^2\right)=4a^2-a^4\)
Bài 2 :
a) \(\left(x+1\right)\left(x^2-x+1\right)=x^3+1\)
b) \(\left(x+y+z\right)^2=\left(x+y+z\right)\left(x+y+z\right)=x^2+xy+xz+yx+y^2+yz+zx+zy+z^2=x^2+2xy+2yz+2xz+y^2+z^2\)
c) \(\left(x-y+z\right)^2=\left(x-y+z\right)\left(x-y+z\right)=x^2-xy+xz-xy+y^2-yz+xz-yz+z^2=x^2+y^2+z^2-2xy+2xz-2yz\)d) \(\left(x-2y\right)\left(x^2+2xy+4y^2\right)=\left(x-2y\right)^3\)
e) \(\left(x-y-z\right)^2=\left(x-y-z\right)\left(x-y-z\right)=x^2-xy-xz-xy+y^2+yz-xz+yz+z^2=x^2-2xy-2xz+2yz+y^2+z^2\)