1: =10(a^3-a)

=10a(a^2-1)

=10a(a-1)(a+1)

2: \(=5xy\left(1-8a^3b^3\right)\)

\(=5xy\left(1-2ab\right)\left(1+2ab+4a^2b^2\right)\)

3: \(=5\left(a^2+2ab+b^2\right)=5\left(a+b\right)^2\)

4: \(=6\left(p^2-2p+1\right)=6\left(p-1\right)^2\)

5: =(m+n)^2-p^2

=(m+n-p)(m+n+p)

6: =2(27x^3+8y^3)

=2(3x+2y)(9x^2-6xy+4y^2)

1) 10a³ - 10a

= 10a(a² - 1)

= 10a(a - 1)(a + 1)

2) 5xy - 40a³b³xy

= 5xy(1 - 8a³b³)

= 5xy(1 - 2ab)(1 + 2ab + 4a²b²)

3) 5a² + 10ab + 5b²

= 5(a² + 2ab + b²)

= 5(a + b)²

4) 6p² - 12p + 6

= 6(p² - 2p + 1)

= 6(p - 1)²

5) m² + 2mn + n² - p²

= (m + n)² - p²

= (m + n - p)(m + n + p)

6) 54x³ + 16y³

= 2(27x³ + 8y³)

= 2[(3x)³ + (2y)³]

= 2(3x + 2y)(9x² - 6xy + 4y²)

7) Sửa đề:

1 - m² + 2mn - n²

= 1 - (m² - 2mn + n²)

= 1 - (m - n)²

= (1 + m - n)(1 - m + n)

a: \(5a^2xy-10a^3x-15axy\)

\(=5ax\left(ay-2a^2-3y\right)\)

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

\(=9-4x^2-4x^2-4x-1\)

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

=5(a-b)²-10(a-b)= (a-b)(5a-5b-10)=5(a-b)(a-b-2)

a) \(3xy^2-12xy+12x\)

\(=3x\left(y-4y+4\right)\)

b) \(3x^3y-6x^2y-3xy^3-6axy^2-3a^2xy+3xy\)

\(=3xy\left(x^2-2x-y^2-2ay-a^2+1\right)\)

\(=3xy\left[\left(x^2-2\cdot x\cdot1+1^2\right)-\left(y^2+2\cdot y\cdot a+a^2\right)\right]\)

\(=3xy\left[\left(x-1\right)^2-\left(y+a\right)^2\right]\)

\(=3xy\left(x-1-y-a\right)\left(x-1+y+a\right)\)

c) \(36-4a^2+20ab-25b^2\)

\(=6^2-\left[\left(2a\right)^2-2\cdot2a\cdot5b+\left(5b\right)^2\right]\)

\(=6^2-\left(2a-5b\right)^2\)

\(=\left(6-2a+5b\right)\left(6+2a-5b\right)\)

d) \(5a^3-10a^2b+5ab^2-10a+10b\)

\(=5a\left(a^2-2ab+b^2\right)-10\left(a-b\right)\)

\(=5a\left(a-b\right)^2-10\left(a-b\right)\)

\(=\left(a-b\right)\left[5a\left(a-b\right)-10\right]\)

\(=5\left(a-b\right)\left[a\left(a-b\right)-2\right]\)

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

a. 3xy²-12xy+12x

= 3x(y²-4y+4)

= 3x(y-2)²

b. 3x³y-6x²y-3xy³-6axy²-3a²xy+3xy

= 3xy( x²-2x-y²-2ay-a²+1)

= 3xy ((x²-2x+1)-(a²-2ay-y²))

=3xy((x-1)²-(a-y)²)

= 3xy((x-1+a-y)(x-1-(a-y))

=3xy(x-1+a-y)(x-1-a+y)

d. =( 5a(a²-2ab+b²))-(10(a+b))

= 5a(a-b)²-10(a-b)

=5a(a-b)(a-b)-10(a-b)

=(a-b)(5a(a-b)-10)

Hình như mik làm sai hết rồi

x²-xy+2x-2y
= (x²-xy)+(2x-2y)
= x(x-y)+2(x-y)
= (x-y)(x+2)

ax+ay-2x-2y
= (ax+ay)-(2x+2y)
= a(x+y)-2(x+y)
=(x+y)(a-2)

ax²-3axy+bx-3by
= (ax²+bx)-(3axy+3by)
= x(ax+b)-3y(ax+b)
= (ax+b)(x-3y)

2a²-5by-5a²y+2bx
= (2a²-5a²y)+(2bx-5by)
= a²(2-5y)+b(2x-5y)

x²-xy+2x-2y=(x²-xy)+(2x-2y)=x(x-y)+2(x-y)=(x-y)(x+2)

ax+ay-2x-2y=(ax+ay)-(2x+2y)=a(x+y)-2(x+y)=(x+y)(a-2)

ax²-3axy+bx-3by=(ax²+bx)-(3axy+3by)=x(ax+b)-3y(ax+b)=(ax+b)(x-3y)