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a) Áp dụng hằng đẳng thức : \(a^2-b^2+\left(a-b\right)\left(a+b\right)\)
Ta có ; \(\left(a^2+2a+3\right)\left(a^2+2a-3\right)\)
\(=\left[\left(a^2+2a\right)+3\right]\left[\left(a^2+2a\right)-3\right]\)
\(=\left(a^2+2a\right)^2-3^2\)
\(=\left(a^2+2a\right)^2-9\)
1:
a: \(\left(x+y+z\right)^2=x^2+y^2+z^2+2xy+2zx+2yz\)
b: \(\left(x-y+z\right)^2=x^2+y^2+z^2-2xy+2xz-2yz\)
c: \(\left(x-y-z\right)^2=x^2+y^2+z^2-2xy-2xz+2yz\)
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) \(\left(x-y-z\right)^2=\left(x-y-z\right)\left(x-y-z\right)=x^2-xy-xz-xy+y^2+yz-xz+yz+z^2=x^2-2xy-2xz+2yz+y^2+z^2\)
( a2 - 2a + 3 )( a2 + 2a - 3 )
= [ a2 - ( 2a - 3 ) ][ a2 + ( 2a - 3 ) ]
= ( a2 )2 - ( 2a - 3 )2
= a4 - ( 4a2 - 12a + 9 )
= a4 - 4a2 + 12a - 9
\(\left(a^2-2a+3\right)\left(a^2+2a-3\right)\)
\(=a^4+2a^3-3a^2-2a^3-4a^2+6a+3a^2+6a-9\)
\(=a^4-4a^2+12a-9\)
a: \(\left(a^2+2a+3\right)\left(a^2-2a-3\right)\)
\(=\left[a^2+\left(2a+3\right)\right]\left[a^2-\left(2a+3\right)\right]\)
\(=\left(a^2\right)^2-\left(2a+3\right)^2\)
\(=a^4-\left(2a+3\right)^2\)
b: \(\left(-a^2-2a+3\right)^2\)
\(=\left(a^2+2a-3\right)^2\)
\(=a^4+4a^2+9+4a^3-18a-6a^2\)
\(=a^4+4a^3-2a^2-18a+9\)
c: \(\left(x-y-z\right)^2\)
\(=x^2-2x\left(y+z\right)+\left(y+z\right)^2\)
\(=x^2-2xy-2xz+y^2+2yz+z^2\)
d: \(\left(x+y+z\right)\left(x-y-z\right)\)
\(=x^2-\left(y+z\right)^2\)
\(=x^2-y^2-2yz-z^2\)
a: \(=a^2-b^4\)
b: \(=\left(a^2+2a\right)^2-9\)
c: \(=a^2-\left(2a+3\right)^2\)
d: \(=a^4-\left(2a-3\right)^2\)
e: \(=\left(-a^2-2a+3\right)^2\)
g: \(=4a^2-a^4\)
\(a^22\) là a2 nhân với 2 đó hả?
\(a,\left(a^22+2a+3\right)\left(a^22+2a-3\right)\)
\(=\left[\left(a^22+2a\right)+3\right]\left[\left(a^22+2a\right)-3\right]\)
\(=\left(a^22+2a\right)^2-9\)
\(=4a^4+8a^3+4a^2-9\)
\(b,\left(a^22+2a+3\right)\left(a^2-2a-3\right)\)
\(=2a^4-4a^3-6a^2+2a^3-4a^2-6a+3a^2-6a-9\)
\(=2a^4-2a^3-7a^2-12a-9\)
\(c,\left(a^22-2a+3\right)\left(a^2+2a-3\right)\)
\(=2a^4+4a^3-6a^2-2a^3-4a^2+6a+3a^2+6a-9\)
\(=2a^4+2a^3-7a^2+12a-9\)
a: \(=\left(-a^2-2a+3\right)^2\)
b: \(=\left(a^2+3\right)^2-4a^2\)
c: \(=-\left(a^2-2a\right)\left(a^2+2a\right)=-\left(a^4-4a^2\right)\)