Phân tích thành nhân tử:
a) x^4+16
b) x^4y^4+64
c) x^4y^4+4
d) 4x^4y^4+1
e) x^4+1
f) x^8+x+1
g) x^8+x^7+1
h) x^8+3x^4+1
k) x^4+4y^4
l) a^2-b^2-2x(a-b)
m) a^2-b^2-2x(a+b)
Phân tích thành nhân tử: a) x^4+16 b) x^4y^4+64 c) x^4y^4+4 d) 4x^4y^4+1 e) x^4+1 f) x^8+x+1 g) x^8+x^7+1 h) x^8+3x^4+1 k) x^4+4y^4 l) a^2-b^2-2x(a-b)
By Lydia
Đáp án:
Giải thích các bước giải:
a) \(x^4+16\)
\(=\left(x^2\right)^2+4^2\)
\(=\left(x^2\right)^2+2x^2.4+4^2-2x^2.4\)
\(=\left(x^2+4\right)^2-8x^2\)
\(=\left(x^2+4\right)^2-\left(2\sqrt{2}x\right)^2\)
\(=\left(x^2+4-2\sqrt{2}x\right)\left(x^2+4+2\sqrt{2}x\right)\)
b) \(x^4y^4+64=x^4y^4+16x^2y^2+64-16x^2y^2=\left(x^2y^2+8\right)^2-16x^2y^2=\left(x^2y^2-4xy+8\right)\left(x^2y^2+4xy+8\right)\)
c) `x^4y^4 + 4`
`= x^4y^4 + 4x^2y^2 + 4 – 4x^2y^2`
`= (x^2y^2 + 2)^2 – (2xy)^2`
`= (x^2y^2 – 2xy + 2)(x^2y^2 + 2xy + 2)`
f) \(x^8+x+1=x^8-x^2+\left(x^2+x+1\right)=x^2\left(x^6-1\right)+\left(x^2+x+1\right)=x^2\left(x^3-1\right)\left(x^3+1\right)+\left(x^2+x+1\right)=x^2\left(x-1\right)\left(x+1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)+x^2+x+1=\left(x^2+x+1\right)\text{[}x^2\left(x+1\right)\left(x-1\right)\left(x^2-x+1\right)+1\text{]}\)
g) x8 + x7 + 1
= x8 + x7 – x6 + x6 + 1
= x6( x2 + x +1) – [ ( x3)2 – 1]
= x6( x2 + x +1) – ( x3 – 1)( x3 + 1)
= x6( x2 + x +1) – ( x -1)( x2 + x +1)( x3 + 1)
= ( x2 + x +1)[x6 – ( x -1)( x3 + 1)]
= ( x2 + x +1)[ x6 – ( x4 + x – x3 – 1)
= ( x2 + x +1)( x6 – x4 – x + x3 – 1)
\(k)x^4+4y^4\)
\(=\left(x^2\right)^2+\left(2y^2\right)^2\)
\(=\left(x^2\right)^2+4x^2y^2+\left(2y^2\right)^2-4x^2y^2\)
\(=\left(x^2+y^2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2+2y^2-2xy\right)\left(x^2+2y^2+2xy\right)\)
l) `a^2-b^2-2x(a-b)`
`= (a-b)(a+b)-2x(a-b)`
`=(a-b)(a+b-2x)`
m) `a^2-b^2-2x(a+b)`
`= (a-b)(a+b)-2x(a+b)`
`=(a+b)(a-b-2x)`