a ) \(3x^2-7x+2\)

   = \(3x^2-6x-x+2\)

  = \(3x\left(x-2\right)-\left(x-2\right)\)

= \(\left(x-2\right)\left(3x-1\right)\)

b ) \(a\left(x^2+1\right)-x\left(a^2+1\right)\)

= \(ax\left(x-a\right)-\left(x-a\right)\)

= \(\left(x-a\right)\left(ax-1\right)\)

Chúc bạn học tốt !!!

Câu 1 : x²-y²+2yz-z²=-(y²-2yz+z²-x²)                    Câu 2: x²-2xy+y²-xz+yz=(x²-2xy+y²)-xz+yz

                                 =-(y-z)² -x²                                                                   =(x-y)²-z(x-y)

                                        =-(y-z-x)(y-z+x)                                                            =(x-y)(x-y-z)

7: \(\left(xy+4\right)^2-\left(2x+2y\right)^2\)

=(xy+4-2x-2y)(xy+4+2x+2y)

=[x(y-2)-2(y-2)][x(y+2)+2(y+2)]

=(x-2)(y-2)(x+2)(y+2)

8: \(81x^2-64y^2=\left(9x\right)^2-\left(8y\right)^2\)

=(9x-8y)(9x+8y)

9: \(\left(a^2+b^2+5\right)^2-4\left(ab+2\right)^2\)

\(=\left(a^2+b^2+5\right)^2-\left(2ab+4\right)^2\)

\(=\left(a^2+b^2+5-2ab-4\right)\left(a^2+b^2+5+2ab+4\right)\)

\(=\left\lbrack\left(a-b\right)^2+1\right\rbrack\left\lbrack\left(a+b\right)^2+9\right\rbrack\)

10: \(\left(x-1\right)^2-\left(x+1\right)^2\)

=(x-1-x-1)(x-1+x+1)

=2x*(-2)=-4x

11: \(8x^3-\frac18=\left(2x\right)^3-\left(\frac12\right)^3=\left(2x-\frac12\right)\left(4x^2+2x\cdot\frac12+\frac14\right)\)

\(=\left(2x-\frac12\right)\left(4x^2+x+\frac14\right)\)

12: \(\frac{1}{25}x^2-64y^2=\left(\frac15x\right)^2-\left(8y\right)^2=\left(\frac15x-8y\right)\left(\frac15x+8y\right)\)

13: \(x^3+\frac{1}{27}=x^3+\left(\frac13\right)^3=\left(x+\frac13\right)\left(x^2-\frac13x+\frac19\right)\)

\(A=x^3-15x^4+16x^3-29x^2\)

\(A=\left(x^3+16x^3\right)-15x^4-29x^2\)

\(A=17x^3-15x^4-29x^2\)

\(A=-15x^4+17x^3-29x^2\)

\(A=-x^2\left(15x^2-17x+29\right)\)

Câu 1: 3x² - 6xy + 3y² - 12z²

= 3(x² - 2xy + y² - 4z²)

= 3[(x² -2xy+y²)- (2z)²]

= 3[(x-y)² - (2z)²]

=3(x-y-2z)(x-y +2z)

Câu 2: x² - 6xy - 25z²+ 9y²

= x² - 2x.3y + (3y)² - (5z)²

= (x-3y)² - (5z)²

= (x-3y-5z)(x-3y+5z) 

Trả lời:

a, x⁴ + 3x³ + x² + 3x

= ( x⁴ + 3x³ ) + ( x² + 3x )

= x³ ( x + 3 ) + x ( x + 3 )

= ( x³ + x ) ( x + 3 )

= x ( x² + 1 ) ( x + 3 )

b, Sửa đề: x⁴ - x² + 8x - 8

= ( x⁴ - x² ) + ( 8x - 8 )

= x² ( x² - 1 ) + 8 ( x - 1 ) 

= x² ( x - 1 ) ( x + 1 ) + 8 ( x - 1 )

= ( x - 1 ) [ x² ( x + 1 ) + 8 ]

= ( x - 1 ) ( x³ + x² + 8 )

x⁴ + 3x³ + x² + 3x = x³(x + 3) + x(x + 3)
= (x + 3)(x² + 1)x

6, \(x^2-1+2xy+y^2=\left(x+y\right)^2-1=\left(x+y-1\right)\left(x+y+1\right)\)

7, \(4x^2-12x+9-y^2=\left(2x-3\right)^2-y^2=\left(2x-3-y\right)\left(2x-3+y\right)\)

8, \(16x^2-4y^2+4y-1=16x^2-\left(2y-1\right)^2=\left(4x-2y+1\right)\left(4x+2y-1\right)\)

9, \(25-x^2-12x-36=25-\left(x+6\right)^2=\left(5-x-6\right)\left(5+x+5\right)=-\left(x+1\right)\left(x+10\right)\)

10, \(x^2-9-5\left(x+3\right)=\left(x-3\right)\left(x+3\right)-5\left(x+3\right)=\left(x+3\right)\left(x-8\right)\)

bạn ơi  bạn viết sai đề có đề nào viết  thế này đâu?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

Uchiha Itachi

7,      4x mũ 2 - 12x + 9 - y mũ 2 =  -(y-2x+3) (y+2x-3)

8,      16x mũ 2 - 4y mũ 2 + 4y - 1 =   -(2y - 4x - 1) (2y+4x-1)

9,        25 - x mũ 2 - 12x - 36 =  -(x+1) (x+11)

10,        x mũ 2 - 9 - 5 ( x + 3 ) =  (x-8) (x+3)

bạn k cho mình nha 

chúc bạn học tốt :))))

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Câu hỏi của Phạm Đỗ Bảo Ngọc - Toán lớp 8 - Học trực tuyến OLM