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a: \(=\left(-a^2-2a+3\right)^2\)
b: \(=\left(a^2+3\right)^2-4a^2\)
c: \(=-\left(a^2-2a\right)\left(a^2+2a\right)=-\left(a^4-4a^2\right)\)
\(a^22\) là a2 nhân với 2 đó hả?
\(a,\left(a^22+2a+3\right)\left(a^22+2a-3\right)\)
\(=\left[\left(a^22+2a\right)+3\right]\left[\left(a^22+2a\right)-3\right]\)
\(=\left(a^22+2a\right)^2-9\)
\(=4a^4+8a^3+4a^2-9\)
\(b,\left(a^22+2a+3\right)\left(a^2-2a-3\right)\)
\(=2a^4-4a^3-6a^2+2a^3-4a^2-6a+3a^2-6a-9\)
\(=2a^4-2a^3-7a^2-12a-9\)
\(c,\left(a^22-2a+3\right)\left(a^2+2a-3\right)\)
\(=2a^4+4a^3-6a^2-2a^3-4a^2+6a+3a^2+6a-9\)
\(=2a^4+2a^3-7a^2+12a-9\)
Bài làm:
Ta có: \(\left(a^2+2a\right)\left(2a-a^2\right)\)
\(=4a^2-a^4\)
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: \(=4a^2-a^4\)
Bài 1:
a) -16 +(x-3)2
<=> (x-3)2-16
<=> (x-3)2 -42
<=> (x-3-4)(x-3+4)
<=> (x-7)(x+1)
b) 64+16y+y2
<=> y2 + 2.8.y + 82
<=> (y+8)2
c) \(\dfrac{1}{8}-8x^3\)
\(\Leftrightarrow\left(\dfrac{1}{2}\right)^3-\left(2x\right)^3\)
\(\Leftrightarrow\left(\dfrac{1}{2}-2x\right)\left(\dfrac{1}{4}+x+4x^2\right)\)
d)\(x^2-x+\dfrac{1}{4}\)
\(\Leftrightarrow x^2-2.\dfrac{1}{2}.x+\left(\dfrac{1}{2}\right)^2\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2\)
e) x4 + 4x2 + 4
<=> (x2)2 + 2.2.x2 +22
<=> (x2 + 2)2
g)\(8x^3+60x^2y+150xy^2+125y^3\)
\(\Leftrightarrow\left(2x+5y\right)^3\)
( 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
\(\left(a^2-2a+3\right)\left(a^2+2a-3\right)\)
\(=a^4+2a^3-3a^2-2a^3-4a^2+6a+3a^2+6a-9\)
\(=a^4-4a^2+12a-9\)