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nirvana33 [79]
3 years ago
11

I will give brainliest to best answerFactorise completely (3x^2-5y^2)​

Mathematics
1 answer:
Artemon [7]3 years ago
6 0
<h2><em>we can write (3x^2-5y^2) as (3x-5y)^2</em></h2><h2><em>( 3 x − 5 y ) 2   as  ( 3 x− 5 y ) ( 3 x− 5 y )</em></h2><h2><em>3 x ( 3 x − 5 y ) − 5 y ( 3x −5 y )</em></h2><h2><em>3 x ( 3 x − 5 y ) − 5 y (3 x − 5 y )</em></h2><h2><em>3 x ( 3 x ) + 3 x ( − 5y ) − 5 y ( 3 x ) − 5 y( -5 y )</em></h2><h2><em>9 x 2 − 15 x y − 15y x + 25 y 2 </em></h2><h2><em>  Subtract  15 y x  from  − 15 x y .</em></h2><h2><em>9 x 2 − 30 xy + 25 y 2</em></h2><h2><em>                                 HOPE IT HELPS(◕‿◕✿)    </em></h2><h2><em>                                             SMILE!!                                                                         </em></h2>
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30 POINTS AVAILABLE
kherson [118]

Answer:

\large\boxed{(x-2)^2+(y-1)^2=34}

Step-by-step explanation:

The equation of a circle in standard form:

(x-h)^2+(y-k)^2=r^2

(h, k) - center

r - radius

We have the endpoints of the diameter: (-1, 6) and (5, -4).

Midpoint of diameter is a center of a circle.

The formula of a midpoint:

\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)

Substitute:

h=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\\k=\dfrac{6+(-4)}{2}=\dfrac{2}{2}=1

The center is in (2, 1).

The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.

The formula of a distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Substitute the coordinates of the points (2, 1) and (5, -4):

r=\sqrt{(5-2)^2+(-4-1)^2}=\sqrt{3^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}

Finally we have:

(x-2)^2+(y-1)^2=(\sqrt{34})^2

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