Question

1) 10a³ - 10a 2) 5xy - 40a³b³ xy 3) 5a² + 10ab + 5b² 4) 6p² - 12p + 6 5) m² + 2mn + n² - p² 6) 54x³ + 16y³ 7) 1 - m² + 2mn - b²

Answer 1

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)

Answer 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)