Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a) x2 – 4x + 3 = x2 – x - 3x + 3
= x(x - 1) - 3(x - 1) = (x -1)(x - 3)
b) x2 + 5x + 4 = x2 + 4x + x + 4
= x(x + 4) + (x + 4)
= (x + 4)(x + 1)
c) x2 – x – 6 = x2 +2x – 3x – 6
= x(x + 2) - 3(x + 2)
= (x + 2)(x - 3)
d) x4+ 4 = x4 + 4x2 + 4 – 4x2
= (x2 + 2)2 – (2x)2
= (x2 + 2 – 2x)(x2 + 2 + 2x)
Bài giải:
a) x2 – 4x + 3 = x2 – x - 3x + 3
= x(x - 1) - 3(x - 1) = (x -1)(x - 3)
b) x2 + 5x + 4 = x2 + 4x + x + 4
= x(x + 4) + (x + 4)
= (x + 4)(x + 1)
c) x2 – x – 6 = x2 +2x – 3x – 6
= x(x + 2) - 3(x + 2)
= (x + 2)(x - 3)
d) x4+ 4 = x4 + 4x2 + 4 – 4x2
= (x2 + 2)2 – (2x)2
= (x2 + 2 – 2x)(x2 + 2 + 2x)
\(g,x^2-2xy+y^2-9z^2=\left(x-y\right)^2-\left(3z\right)^2\)\(=\left(x-y+3z\right)\left(x-y-3z\right)\)
\(h,5x^4-20x^2=5x^2\left(x^2-4\right)=5x^2\left(x-2\right)\left(x+2\right)\)
\(i,7x^2-7y^2-14x+14y=7\left(x-y\right)\left(x+y\right)-14\left(x-y\right)\)
\(=\left(x-y\right)\left(7x+7y-14\right)=7\left(x-y\right)\left(x+y-2\right)\)
\(k,x^2+8x+3x+24=x\left(x+8\right)+3\left(x+8\right)=\left(x+8\right)\left(x+3\right)\)
\(m,x^4-y^4=\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)
\(n,x^6-y^6=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)=\left(x-y\right)\left(x+y\right)\left(x^4+x^2y^2+y^4\right)\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
a) \(3x^2-9x+30=3\left(x^2-3x+10\right)\)
b) \(3x^2-5x-2=3x^2-6x+x-2\)
\(=3x\left(x-2\right)+\left(x-2\right)=\left(3x+1\right)\left(x-2\right)\)
c) \(x^4+4y^4\)
\(=x^4+4y^4+2x^2y^2+2x^2y^2-4x^2y^2+4xy^3-4xy^3+2x^3y-2x^3y\)
\(=\left(4y^4-4xy^3+2x^2y^2\right)+\left(4xy^3-4x^2y^2+2x^3y\right)\)
\(+\left(2x^2y^2-2x^3y+x^4\right)\)
\(=2y^2\left(2y^2-2xy+x^2\right)+2xy\left(2y^2-2xy+x^2\right)\)
\(+x^2\left(2y^2-2xy+x^2\right)\)
\(=\left(2y^2+2xy+x^2\right)\left(2y^2-2xy+x^2\right)\)
d) \(x^5+x+1\)
\(=x^5+x+1+x^4-x^4+x^3-x^3+x^2-x^2\)
\(=\left(x^5-x^4+x^2\right)+\left(x^4-x^3+x\right)+\left(x^3-x^2+1\right)\)
\(=x^2\left(x^3-x^2+1\right)+x\left(x^3-x^2+1\right)+\left(x^3-x^2+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
\(C=x^3+5x^2+8x+4\)
\(=x^3+x^2+4x^2+4x+4x+4\)
\(=x^2\left(x+1\right)+4x\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x^2+4x+4\right)\left(x+1\right)\)
\(=\left(x+2\right)^2.\left(x+1\right)\)
\(D=x^3-x^2-4\)
\(=x^3-2x^2+x^2-2x+2x-4\)
\(=x^2\left(x-2\right)+x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x^2+x+2\right)\left(x-2\right)\)
Chúc bạn học tốt.
Trả lời:
1) sửa đề: \(x^4+x^3-4x-4=x^3\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x^3-4\right)\)
2) \(x^2-\left(a+b\right)x+ab=x^2-ax-bx+ab=\left(x^2-ax\right)-\left(bx-ab\right)\)
\(=x\left(x-a\right)-b\left(x-a\right)=\left(x-a\right)\left(a-b\right)\)
3) \(5xy^3-2xyz-15y^2+6z=\left(5xy^3-15y^2\right)-\left(2xyz-6z\right)\)
\(=5y^2\left(xy-3\right)-2z\left(xy-3\right)=\left(xy-3\right)\left(5y^2-2z\right)\)
27x6 + 125y6 = ( 3x2 )3 + ( 5y2 )3 = ( 3x2 + 5y2 )( 9x4 - 15x2y2 + 25y4 )
8a6 - 8b6 = ( 2a2 )3 - ( 2b2 )3 = ( 2a - 2b )( 4a2 + 4ab + 4b2 ) = 2( a - b )4( a2 + ab + b2 ) = 8( a - b )( a2 + ab + b2 )
x4 + 64y4 = x4 + 16x2y2 + 64y4 - 16x2y2
= ( x4 + 16x2y2 + 64y4 ) - 16x2y2
= ( x2 + 8y2 )2 - ( 4xy )2
= ( x2 + 8y2 - 4xy )( x2 + 8y2 + 4xy )
x4 + x3 + 2x2 + x + 1 = x4 + x3 + x2 + x2 + x + 1
= ( x4 + x3 + x2 ) + ( x2 + x + 1 )
= x2( x2 + x + 1 ) + ( x2 + x + 1 )
= ( x2 + x + 1 )( x2 + 1 )
\(27x^6+125y^6=\left(3x^2\right)^3+\left(5y^2\right)^3=\left(3x^2+5y^2\right)\left(9x^4-15x^2.y^2+25y^4\right)\)
\(8a^6-8b^6=8\left(a^6-b^6\right)=8\left(\left(a^3\right)^2-\left(b^3\right)^2\right)=8\left(a^3-b^3\right)\left(a^3+b^3\right)\)
\(=8\left(a-b\right)\left(a^2+ab+b^2\right)\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(x^{\text{4}}+64y^4=x^4+64y^4+16x^2y^2-16x^2y^2\)
\(=\left(8y^2+x^2\right)^2-\left(4xy\right)^2=\left(8y^2+x^2+4xy\right)\left(8y^2+x^2-4xy\right)\)
\(x^4+x^3+2x^2+x+1=\left(x^4+2x^2+1\right)+\left(x^3+x\right)\)
\(=\left(x^2+1\right)^2+x\left(x^2+1\right)=\left(x^2+1\right)\left(x^2+x+1\right)\)
\(x^2-\text{5}xy-14y^2\)
\(=x^2+2xy-7xy-14y^2\)
\(=x\left(x+2y\right)-7y\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-7y\right)\)
a) \(x^2-5xy-14y^2=x^2-7xy+2xy-14y^2\)
\(=\left(x-7y\right)\left(x+2y\right)\)
b) \(x^2-5x+6=x^2-2x-3x+6=\left(x-2\right)\left(x-3\right)\)
c) \(x^4+4=x^4+4x^2+4-\left(2x\right)^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
d)