Question

А) 3x2 - 12 = б) 2x2 - 98a2 = в) bx2 - 9b = г) -3a + 3p2a = д) 9x3 - 9a2x =

Answer 1

Ответ:

Объяснение:

a) 3x^-12 = 3(x^2-4) = 3(x-2)(x+2)

б) 2x^2 - 98a^2=2(x^2-49a^2) = 2(x-49a)(x+49a)

в)bx^2-9b=b(x-3)(x+3)

г) -3a+3p^2a=3a(-1+p^2)=3a(p-1)(p+1)

д) 9x^3-9a^2x=9x(x^2-a^2)= 9x(x-a)(x+a)

Answer 2

To solve each of the equations, let's go through them one by one:

a) 3x^2 - 12 = 0

To solve this quadratic equation, we can factor it: 3x^2 - 12 = 0 3(x^2 - 4) = 0 (x^2 - 4) = 0

Now, we have a difference of squares, which can be factored further: (x - 2)(x + 2) = 0

Setting each factor equal to zero: x - 2 = 0 or x + 2 = 0

Solving for x in each case: x = 2 or x = -2

Therefore, the solutions to the equation are x = 2 and x = -2.

b) 2x^2 - 98a^2 = 0

To solve this quadratic equation, we can factor out the common factor: 2(x^2 - 49a^2) = 0

Again, we have a difference of squares, which can be factored further: 2(x - 7a)(x + 7a) = 0

Setting each factor equal to zero: x - 7a = 0 or x + 7a = 0

Solving for x in each case: x = 7a or x = -7a

Therefore, the solutions to the equation are x = 7a and x = -7a.

c) bx^2 - 9b = 0

To solve this quadratic equation, we can factor out the common factor: b(x^2 - 9) = 0

Once again, we have a difference of squares: b(x - 3)(x + 3) = 0

Setting each factor equal to zero: x - 3 = 0 or x + 3 = 0

Solving for x in each case: x = 3 or x = -3

Therefore, the solutions to the equation are x = 3 and x = -3.

d) -3a + 3p^2a = 0

To solve this equation, we can factor out the common factor: -3a(1 - p^2) = 0

Setting each factor equal to zero: -3a = 0 or 1 - p^2 = 0

Solving for a in the first case: a = 0

Solving for p in the second case: 1 - p^2 = 0 p^2 = 1 p = ±1

Therefore, the solutions to the equation are a = 0 and p = ±1.

e) 9x^3 - 9a^2x = 0

To solve this equation, we can factor out the common factor: 9x(x^2 - a^2) = 0

We have a difference of squares, which can be factored further: 9x(x - a)(x + a) = 0

Setting each factor equal to zero: x - a = 0 or x + a = 0 or x = 0

Solving for x in each case: x = a or x = -a or x = 0

Therefore, the solutions to the equation are x = a, x = -a, and x = 0.