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1)7x(x-5)-x(x-5)=(x-5)(7x-x)=6x(x-5)
2)x4+3x3+x+3=x3(x+3)+(x+3)=(x+3)(x3+1)=(x+3)(x+1)(x2-x+1)
3)x4+64=[(x2)2+2.x2.8+64]-16x2=(x2+8)2-(4x)2=(x2+4x+8)(x2-4x+8)
\(x^4+4x^2-5\)
\(=\left(x^4+4x^2+4\right)-9\)
\(=\left(x^2+2\right)^2-9\)
\(=\left(x^2+2+3\right)\left(x^2+2-3\right)\)
\(=\left(x^2+5\right)\left(x^2-1\right)\)
A) 1/2 x(x^2-4)+4(x+2)
=1/2x(x-2)(x+2)+4(x+2)
=(x+2)(1/2x^2-x+4)
b) 21(x-y)^2-7(x-y)^3
= (x-y)^2(21-7x+7y)
=(x-y)^2.7(3-x+y)
c) 1/8x^3-3/4x^2+3/2x-1
=(1/2x)^3-3.(1/2x)^2.1+3.1/2x.1^2-1
=(1/2x-1)^3
Bạn hội con bò gì đó ơi cho mk tham gia đc không vì là hội học hành nên .....
a) \(x^3+2x^2+2x+1\)
\(=\left(x^3+x^2\right)+\left(x^2+x\right)+\left(x+1\right)\)
\(=x^2\left(x+1\right)+x\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+x+1\right)\)
b) \(x^3+x^2-4x-4\)
\(=x^2\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-4\right)\)
\(=\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
c) \(x^4-2x^3+2x-1\)
\(=\left(x^4-x^3\right)-\left(x^3-x^2\right)-\left(x^2-x\right)+\left(x-1\right)\)
\(=x^3\left(x-1\right)-x^2\left(x-1\right)-x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3-x^2-x+1\right)\)
\(=\left(x-1\right)\left[x^2\left(x-1\right)-\left(x-1\right)\right]\)
\(=\left(x-1\right)\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)^3\left(x+1\right)\)
d) \(x^5-x^4+x^3-x^2\)
\(=x^4\left(x-1\right)+x^2\left(x-1\right)\)
\(=x^2\left(x-1\right)\left(x^2+1\right)\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
\(x^3+x^2+4=x^3+2x^2-x^2-2x+2x+4\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+2\left(x+2\right)\)
\(=\left(x^2-x+2\right)\left(x+2\right)\)
\(x^8+64=x^8+16x^4+64-16x^4\)
\(=\left(x^4+8\right)^2-\left(4x^2\right)^2\)
\(=\left(x^4-4x^2+8\right)\left(x^4+4x^2+8\right)\)
\(4a^4+b^4=4a^4+4a^2b^2+b^4-4a^2b^2\)
\(=\left(2a^2+b^2\right)^2-\left(2ab\right)^2\)
\(=\left(2a^2+b^2-2ab\right)\left(2a^2+b^2+2ab\right)\)
\(x^3-2x-4=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x^2+2x+2\right)\left(x-2\right)\)
Chúc bạn học tốt.