What does 6x^2 - 24y^2 equal too

1 answer:

7 0

Simplify the following:
6 x^2 - 24 y^2

Factor 6 out of 6 x^2 - 24 y^2:
6 (x^2 - 4 y^2)

x^2 - 4 y^2 = x^2 - (2 y)^2:
6 (x^2 - (2 y)^2)

Factor the difference of two squares. x^2 - (2 y)^2 = (x - 2 y) (x + 2 y):
Answer: 6 (x - 2 y) (x + 2 y)

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Answer:

Option c

Step-by-step explanation:

A system of equations are given to us. And we need to solve them . The given system is

$\begin{cases} y = 2x - 3\dots 1 \\ y = x^2 - 3\dots 2 \end{cases}$

We numbered the equations here . Now put the value of equation 1 in equation 2 that is substituting y = 2x - 3 in eq. 2 .

$\implies y = x^2 - 3 \\\\\implies 2x - 3 = x^2 - 3 \\\\\implies x^2 - 2x = 0 \\\\\implies x(x-2) = 0 \\\\\implies\red{ x = 0 , 2 }$

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$\implies y = 2 x - 3 \\\\\implies y = 2(0)-3 \qquad or \qquad y = 2(2)-3 \\\\\implies y = 0-3 \qquad or \qquad 4 - 3 \\\\\implies \red{ y = -3 , 1 }$