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VN
1
17 tháng 8 2016
\(\left(x+1\right)\left(x^2-x-x^2+x-1\right)=-\left(x+1\right)\)
\(\left(2a^2+1\right)^2-4a^2-\left(2a^2+1\right)^2=-4a^2\)
\(\left(a^2+b^2+c^2+a^2-b^2-c^2\right)\left(a^2+b^2+c^2-a^2+b^2+c^2\right)=2a^2\left(2b^2+2c^2\right)=4a^2b^2+4a^2c^2\)
\(\left(a-5\right)^2\left(a+5\right)^2=\left(a^2-25\right)^2\)
\(\left(3a^3+1\right)^2-9a^2-\left(3a^3+1\right)^2=-9a^2\)
19 tháng 6 2019
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) \(\left(a^2+2a\right)\left(2a-a^2\right)=4a^2-a^4\)
19 tháng 6 2019
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) \(\left(x-y-z\right)^2=\left(x-y-z\right)\left(x-y-z\right)=x^2-xy-xz-xy+y^2+yz-xz+yz+z^2=x^2-2xy-2xz+2yz+y^2+z^2\)
TN
1
8 tháng 6 2018
a) Áp dụng hằng đẳng thức : \(a^2-b^2+\left(a-b\right)\left(a+b\right)\)
Ta có ; \(\left(a^2+2a+3\right)\left(a^2+2a-3\right)\)
\(=\left[\left(a^2+2a\right)+3\right]\left[\left(a^2+2a\right)-3\right]\)
\(=\left(a^2+2a\right)^2-3^2\)
\(=\left(a^2+2a\right)^2-9\)
G
14 tháng 8 2020
a) \(A=\left(x-y\right)^2+\left(x+y\right)^2\)
\(=\left(x^2-2xy+y^2\right)+\left(x^2+2xy+y^2\right)\)
\(=x^2-2xy+y^2+x^2+2xy+y^2\)
\(=\left(x^2+x^2\right)-\left(2xy-2xy\right)+\left(y^2+y^2\right)\)
\(=2x^2+2y^2\)
\(=2.\left(x^2+y^2\right)\)
b) \(B=\left(2a+b\right)^2-\left(2a-b\right)^2\)
\(=\left(4a^2+4ab+b^2\right)-\left(4a^2-4ab+b^2\right)\)
\(=4a^2+4ab+b^2-4a^2+4ab-b^2\)
\(=\left(4a^2-4a^2\right)+\left(4ab+4ab\right)+\left(b^2-b^2\right)\)
\(=8ab\)\
c) \(C=\left(x+y\right)^2-\left(x-y\right)^2\)
\(=\left(x^2+2xy+y^2\right)-\left(x^2-2xy+y^2\right)\)
\(=x^2+2xy+y^2-x^2+2xy-y^2\)
\(=\left(x^2-x^2\right)+\left(2xy+2xy\right)+\left(y^2-y^2\right)\)
\(=4xy\)
d) \(D=\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=\left(4x^2-4x+1\right)-2\left(4x^2-12x+9\right)+4\)
\(=4x^2-4x+1-8x^2+24x-18+4\)
\(=\left(4x^2-8x^2\right)-\left(4x-24x\right)+\left(1-18+4\right)\)
\(=-4x^2+20x-13\)
\(=-4x^2+20x-25+12\)
\(=-\left(4x^2-20x+25\right)-8\)
\(=-\left[\left(2x\right)^2-2.4x.5+5^2\right]-8\)
\(=-\left(2x-5\right)^2-8\)
a/ \(16a^4+48a^3+4a^2-120a-72\)
b.\(2b^2+2a^2=4a\)