What is the factored form of the expression over the complex numbers? 4x2+25y2?

Mathematics

2 answers:

Helen [10]2 years ago

4 0

The factored form is 25y^2 + 8 if the 2 was supposed to be an exponent.

Rzqust [24]2 years ago

3 0

Answer:

$(2x+5iy)(2x-5iy)$

Step-by-step explanation:

If a and b are two positive numbers, then

$a^2+b^2=(a+ib)(a-ib)$ .... (1)

The given expression is

$4x^2+25y^2$

It can be rewritten as

$2^2x^2+5^2y^2$

Using distributive property of exponent we get

$(2x)^2+(5y)^2$ $[\because a^mb^m=(ab)^m]$

Using formula (1) we get

$(2x+5iy)(2x-5iy)$ $[\because a^mb^m=(ab)^m]$

Therefore, the factored form of the given expression is $(2x+5iy)(2x-5iy)$ .

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CAN SOMEONE PLEASE WRITE A EQUATION OF THIS LINE!!

serious [3.7K]

Answer (assuming it can be in slope-intercept form):

y = -x - 1

Step-by-step explanation:

When knowing the slope of a line and its y-intercept, you can write an equation to represent it in slope-intercept form, or y = mx + b format. Substitute the m and b for real values.

1) First, find the slope of the equation, or m. Pick any two points from the line and substitute their x and y values into the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$ . I chose the points (0, -1) and (-1, 0):

$m = \frac{(0)-(-1)}{(-1)-(0)} \\m = \frac{0+1}{-1-0} \\m = \frac{1}{-1} \\m = -1$

Thus, the slope is -1.

2) Now, find the y-intercept, or b. The y-intercept of a line is the point at which the line crosses the y-axis. By reading the graph, we can see that the line intersects the y-axis at the point (0,-1), therefore that must be the y-intercept.

3) Now, substitute the found values into the y = mx + b formula. Substitute -1 for m and -1 for b:

$y = -x -1$