Question

1)9x²-25y²=2)(x²+2y)²=3)27x^3+8y^3=4)(5x-6y)=5)x^6-y^3=​

Answer 1

1)9x^2 - 25y^2=(3x-5y)(3x+5y),  

9x^2+30xy+25y^2=(3x+5y)^2.

2)x2 - y2 = (x - y)(x + y)

x2 + y2 = здесь нет такой формулы

3) ((27*x^3+8*y^3)/(9*x^2-6*x*y+4*y^2))-3*x =((3*x+2*y)*(9*x^2-6*x*y+4*y^2))/(9*x^2-6*x*y+4*y^2)-3*x=(3*x+2*y-3*x)=2*y;

4)= (5x - 6y - 5x - 6y)(5x - 6y + 5x + 6y) =  

= - 12y * 10x =  

= - 120xy

5)4x+3y-36=0

3y=36-4x | /3

y=12-4x/3

x-6y+3=0

6y=x+3

y=x+3/6

Answer 2

To solve the given equations, I'll break them down one by one:

1. 9x² - 25y² = 0

This equation represents a difference of squares. We can factor it as follows:

9x² - 25y² = (3x + 5y)(3x - 5y) = 0

Now, we have two possibilities:

a) 3x + 5y = 0 b) 3x - 5y = 0

2. (x² + 2y)² = 0

This equation is also a difference of squares:

(x² + 2y)² = (x² + 2y)(x² + 2y) = 0

Now, we have:

x² + 2y = 0

3. 27x³ + 8y³ = 0

This equation is a sum of cubes:

27x³ + 8y³ = (3x)^3 + (2y)^3 = (3x + 2y)(9x² - 6xy + 4y²) = 0

Now, we have two possibilities:

a) 3x + 2y = 0 b) 9x² - 6xy + 4y² = 0

4. 5x - 6y = 0

This equation represents a linear equation, which can be solved directly:

5x - 6y = 0 5x = 6y x = (6/5)y

5. x⁶ - y³ = 0

This equation is also a difference of cubes:

x⁶ - y³ = (x²)³ - (y)³ = (x² - y)(x⁴ + x²y + y²) = 0

Now, we have two possibilities:

a) x² - y = 0 b) x⁴ + x²y + y² = 0

These are the possible solutions for each equation. Depending on the context or further restrictions, you may need to find specific solutions for each equation.