Explanation

2a³ - a³ = (2-1)a³ = 1a³ = a³

This is because when you subtract a³ from 2a³, you are essentially subtracting 1a³ from 2a³, leaving you with 1a³, which simplifies to a³.

Explanation

The Differential Equation ydx-2xdy=0 represents the family of 'Parabola'.

Explanation

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.

For example, 3x² − 2xy + c is an algebraic expression.

Explanation

If y is directly proportional to x², it means that:

y ∝ x²

This can be written as an equation:

y = kx²

where k is the constant of proportionality.

Given Information:

We are given that y = m for a particular value of x. Let's call this value x₁.

So, we have:

m = kx₁²

Doubling the Value of x:

Now, we double the value of x. Let's call this new value x₂. So, x₂ = 2x₁.

We want to find the new value of y, let's call it y₂, when x = x₂.

Using the proportionality equation:

y₂ = kx₂²

Substitute x₂ = 2x₁:

y₂ = k(2x₁)²

y₂ = 4kx₁²

Substituting the value of kx₁² from the first equation:

We know that kx₁² = m. So, we can substitute this into the equation for y₂:

y₂ = 4m

Explanation

A + B = 15 ... (1)

A - B = 3 ... (2)

Adding (1) and (2), we get:

2A = 18

A = 9

Substituting A into (1), we get:

9 + B = 15

B = 6

Now that we have the values of A and B, we can find the value of AB:

AB = 9 × 6 = 54

Finally, we can find the value of 4AB:

4AB = 4 × 54 = 216

Explanation

Since x varies inversely with y, we can write the equation:

x = k/y

where k is a constant.

Given that x = 4 when y = 16, we can find the value of k:

4 = k/16

k = 64

Now, we can find the value of x when y = 8:

x = 64/8

x = 8

So, the correct answer is: 8

Explanation

The expression x³ + 27 can be factored using the sum of cubes formula:

x³ + 27 = x³ + 3³

= (x + 3)(x² - 3x + 9)

Explanation

j¹⁰⁵ = j^(4*26 + 1) 

= (j⁴)^26 * j¹ 

= 1²⁶ * j 

= j.

Explanation

(20 - X) / 5 = 4

Multiply both sides by 5:

20 - X = 20

Subtract 20 from both sides:

-X = 0

Multiply both sides by -1:

X = 0

So, the value of X is 0.

Explanation

The formula for the difference of squares is 𝑎² − 𝑏² = (𝑎 − 𝑏)(𝑎 + 𝑏).