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a) \(x^4+324=\left(x^2-6x+18\right)\left(x^2+6x+18\right)\)
c) \(x^{13}+x^5+1=\left(x^2+x+1\right)\left(x^{11}-x^{10}+x^8-x^7+x^5-x^4+x^3-x+1\right)\)
d) \(x^{11}+x+1=\left(x^2+x+1\right)\left(x^9-x^8+x^6-x^5+x^3-x^2+1\right)\)
e) \(x^8+3x^4+4=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
khó quá mk nản chí rùi huhu!!
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a)\(x^4+64=x^4+16x^2+64-16x^2\)
\(=\left(x^2\right)^2+2.x^2.8+8^2-\left(4x\right)^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)
b)\(4x^4+81=4x^4+36x^2+81-36x^2\)
\(=\left(2x^2\right)^2+2.2x^2.9+9^2-\left(6x\right)^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
c)\(x^4y^4+64=x^4y^4+16\left(xy\right)^2+64-16\left(xy\right)^2\)
\(=\left[\left(xy\right)^2\right]^2+2.\left(xy\right)^2.8+8^2-\left(8xy\right)^2\)
\(=\left[\left(xy\right)^2+8\right]^2-\left(8xy\right)^2\)
\(=\left[\left(xy\right)^2+8-8xy\right]\left[\left(xy\right)^2+8+8xy\right]\)
Lời giải:
a) $64x^4+81=(8x^2)^2+9^2=(8x^2)^2+9^2+2.8x^2.9-144x^2$
$=(8x^2+9)^2-(12x)^2=(8x^2+9-12x)(8x^2+9+12x)$
b)
$x^8+4y^4=(x^4)^2+(2y^2)^2=(x^4)^2+(2y^2)^2+2.x^4.2y^2-4x^4y^2$
$=(x^4+2y^2)^2-(2x^2y)^2=(x^4+2y^2-2x^2y)(x^4+2y^2+2x^2y)$
c)
$x^8+x^7+1=(x^8-x^2)+(x^7-x)+(x^2+x+1)$
$=x^2(x^6-1)+x(x^6-1)+(x^2+x+1)=(x^6-1)(x^2+x)+(x^2+x+1)$
$=(x^3-1)(x^3+1)(x^2+x)+(x^2+x+1)$
$=(x-1)(x^2+x+1)(x^3+1)(x^2+x)+(x^2+x+1)$
$=(x^2+x+1)[(x-1)(x^3+1)(x^2+x)+1]$
$=(x^2+x+1)(x^6-x^4+x^3-x+1)$