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a: Ta có: \(10x^4-27x^3y-110x^2y^2-27xy^3+10y^4\)

\(=10x^4+20x^2y^2+10y^4-27xy\left(x^2+y^2\right)-130x^2y^2\)

\(=10\left(x^2+y^2\right)^2-27xy\left(x^2+y^2\right)-130x^2y^2\)

\(=10\left(x^2+y^2\right)^2-52xy\left(x^2+y^2\right)+25xy\left(x^2+y^2\right)-130x^2y^2\)

\(=2\left(x^2+y^2\right)\left(5x^2+5y^2-26xy\right)+5xy\left(5x^2+5y^2-26xy\right)\)

\(=\left(5x^2-26xy+5y^2\right)\left(2x^2+5xy+2y^2\right)\)

\(=\left(5x^2-25xy-xy+5y^2\right)\left(2x^2+4xy+xy+2y^2\right)\)

\(=\left\lbrack5x\left(x-5y\right)-y\left(x-5y\right)\right\rbrack\left\lbrack2x\left(x+2y\right)+y\left(x+2y\right)\right\rbrack\)

=(5x-y)(x-5y)(2x+y)(x+2y)

b: \(x^5-4x^4+3x^3+3x^2-4x+1\)

\(=x^5+x^4-5x^4-5x^3+8x^3+8x^2-5x^2-5x+x+1\)

\(=\left(x+1\right)\left(x^4-5x^3+8x^2-5x+1\right)\)

\(=\left(x+1\right)\left(x^4-x^3-4x^3+4x^2+4x^2-4x-x+1\right)\)

\(=\left(x+1\right)\left(x-1\right)\left(x^3-4x^2+4x-1\right)\)

\(=\left(x+1\right)\left(x-1\right)\left\lbrack\left(x^3-x^2\right)-3x^2+3x+x-1\right\rbrack\)

\(=\left(x+1\right)\left(x-1\right)\cdot\left(x-1\right)\left(x^2-3x+1\right)=\left(x+1\right)\left(x-1\right)^2\cdot\left(x^2-3x+1\right)\)

20 tháng 10 2018

tách ra như bth ấy

20 tháng 10 2018

Câu 1 :

a) \(x^3-5x^2-14x\)

\(=x^3-7x^2+2x^2-14x\)

\(=x^2\left(x-7\right)+2x\left(x-7\right)\)

\(=\left(x-7\right)\left(x^2+2x\right)\)

\(=x\left(x-7\right)\left(x+2\right)\)

b) \(a^4+a^2+1\)

\(=\left(a^2\right)^2+2a^2+1-a^2\)

\(=\left(a^2+1\right)-a^2\)

\(=\left(a^2-a+1\right)\left(a^2+a+1\right)\)

c) \(x^4+64\)

\(=\left(x^2\right)^2+2\cdot x^2\cdot8+8^2-2\cdot x^2\cdot8\)

\(=\left(x^2+8\right)^2-\left(4x\right)^2\)

\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)

Câu 2 :

a) \(\left(a-b\right)^2=a^2-2ab+b^2\)

Ta có : \(\left(a+b\right)^2=a^2+2ab+b^2\)

\(\Rightarrow a^2+b^2=\left(a+b\right)^2-2ab=7^2-2\cdot14=25\)

\(\Rightarrow\left(a-b\right)^2=25-2\cdot12=1\)

b) tương tự

9 tháng 3 2019

\(a^4+8a^3+14a^2-8a-15\)

\(=a^4+8a^3+15a^2-a^2-8a-15\)

\(=a^2\left(a^2+8a+15\right)-\left(a^2+8a+15\right)\)

\(=\left(a^2+8a+15\right)\left(a^2-1\right)\)

\(=\left(a+3\right)\left(a+5\right)\left(a-1\right)\left(a+1\right)\)

4 tháng 8 2017

a, \(x^4-x^3-x^3+x^2-x^2+x+x-1\)\(1\)

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

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

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

=\(a^2b^2-2ab+1+a^2+2ab+b^2\)

=\(a^2b^2+a^2+b^2+1\)

=\(a^2\left(b^2+1\right)+\left(b^2+1\right)\)

=\(\left(b^2+1\right)\left(a^2+1\right)\)

c,\(x^4+2x^3+2x^2+2x+1\)

=\(x^4+x^3+x^3+x^2+x^2+x+x+1\)

=\(x^3\left(x+1\right)+x^2\left(x+1\right)+x\left(x+1\right)+\left(x+1\right)\)

=\(\left(x+1\right)\left(x^3+x^2+x+1\right)\)

=\(\left(x+1\right)^2\left(x^2+1\right)\)

26 tháng 8 2021

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)  \(5xy^3-2xyz-15y^2+6z=\left(5xy^3-15y^2\right)-\left(2xyz-6z\right)\)

\(=5y^2\left(xy-3\right)-2z\left(xy-3\right)=\left(xy-3\right)\left(5y^2-2z\right)\)

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

\(\Leftrightarrow\left(x+1-x+1\right)\left(x+1+x-1\right)\)

\(\Leftrightarrow2.2x=4x\)

p/s tham khảo nha

\(a^2-b^2-a+b\)

\(\Leftrightarrow\left(a-b\right)\left(a+b\right)-\left(a-b\right)\)

\(\Leftrightarrow\left(a-b\right)\left(a+b-1\right)\)

p/s tham khảo

20 tháng 4 2017

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)


20 tháng 4 2017

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)

18 tháng 8

Bạn tách ra thành các dòng để bọn mình dễ nhìn hơn nhé.

a:Sửa đề: \(\left(2x+5\right)^2-\left(x-3\right)^2\)

=(2x+5-x+3)(2x+5+x-3)

=(x+8)(3x+2)

b:Sửa đề: \(25\left(2x-1\right)^2-9\left(x+1\right)^2\)

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

=(10x-5-3x-3)(10x-5+3x+3)

=(7x-8)(13x-2)

c: \(1-9x+27x^2-27x^3\)

\(=1^3-3\cdot1^2\cdot3x+3\cdot1\cdot\left(3x\right)^2-\left(3x\right)^3\)

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

d: \(49-a^2+2ab-b^2\)

\(=7^2-\left(a-b\right)^2\)

=(7-a+b)(7+a-b)

e: \(-4x^2-12xy-9y^2+25\)

\(=25-\left(4x^2+12xy+9y^2\right)\)

\(=5^2-\left(2x+3y\right)^2\)

=(5-2x-3y)(5+2x+3y)