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Ta có:
x^4 + 64 = (x²)² + 8² + 2x².8 - 2.x².8
= (x² + 8)² - (4x)²
= (x² - 4x + 8)(x² + 4x + 8)
Ta có:
x^4 + 64 = (x²)² + 8² + 2x².8 - 2.x².8
= (x² + 8)² - (4x)²
= (x² - 4x + 8)(x² + 4x + 8)
\(a,x^2+2xy-9+y^2\)
\(=x^2+2xy+y^2-9\)
\(=\left(x+y\right)^2-9\)
\(=\left(x+y+9\right)\left(x+y-9\right)\)
\(b,x^4+64\)
\(=\left(x^2\right)^2+16x^2+64-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2+8-4x\right)\left(x^2+4x+8\right)\)
Ta có:
x^4 + 64 = (x²)² + 8² + 2x².8 - 2.x².8
= (x² + 8)² - (4x)²
= (x² - 4x + 8)(x² + 4x + 8)
k nhoa
Ta có:
x^4 + 64 = (x²)² + 8² + 2x².8 - 2.x².8
= (x² + 8)² - (4x)²
= (x² - 4x + 8)(x² + 4x + 8)
k nhoa
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)\(x^4y^4+64=x^4y^4+16\left(xy\right)^2+64-16\left(xy\right)^2\)
\(=\left[\left(xy\right)^2\right]^2+2.\left(xy\right)^2.8+8^2-\left(8xy\right)^2\)
\(=\left[\left(xy\right)^2+8\right]^2-\left(8xy\right)^2\)
\(=\left[\left(xy\right)^2+8-8xy\right]\left[\left(xy\right)^2+8+8xy\right]\)
x4y4+64=x4y4+16x2y2+64-16x2y2
=(x2y2+8)2-16x2y2
=(x2y2-4xy+8)(x2y2+4xy+8)