Question

Диктант 17

Применение различных разложения многочлена на множители :
Разложите на множители многочлен:
1)3a²-3b²

2) 6x²-24

3)3x³-9x

4)b⁴-625

5)-3x²+30x-75

6)63y³-84y²z+28yz²

7)a³+a²-9a-9

8)a²+2ab+b²-c²

Answer 1

$\displaystyle \tt 1) \: 3a^2-3b^2=3(a^2-b^2)=3(a-b)(a+b)\\2) \: 6x^2-24=6(x^2-4)=6(x-2)(x+2)\\3) \: 3x^3-9x=3x(x^2-3)\\4) \: b^4-625=(b-5)(b+5)(b^2+25)\\5) \: -3x^2+30x-75=-3(x-5)^2=-3(x-5)(x-5)\\6) \: 63y^3-84y^2z+28yz^2=7y(3y-2z)^2=7y(3y-2z)(3y-2z)\\7) \: a^3+a^2-9a-9=a^2(a+1)-9(a+1)=(a+1)(a^2-9)=(a+1)(a-3)(a+3)\\8) \: a^2+2ab+b^2-c=(a+b-c)(a+b+c)$

Answer 2

$3( {a}^{2} + {b)}^{2} = 3(a - b)(a + b)$

$6( {x}^{2} - 4) = 6(x - 2)(x + 2)$$3x( {x}^{2} - 3) = 3x(x - \sqrt{3} )(x + \sqrt{3} )$$( {b}^{2} - 25)( {b}^{2} + 25) = ( b - 5)(b + 5)( {b}^{2} + 25)$$- 3( {x}^{2} - 10x + 25) = - 3 {(x - 5)}^{2}$$7y(9 {y}^{2} - 12yz + 4 {z}^{2} ) = 7y {(3y - 2z)}^{2}$${a}^{2} (a + 1) - 9(a + 1) = (a + 1)( {a}^{2} - 9) = (a + 1)(a - 3)(a + 3)$${(a + b)}^{2} - {c}^{2} = (a + b - c)(a + b + c)$