Question

(m+4n)^2= 8x^3+1= (2a-3b)^2= Если можно с подробными объяснениями Спасибо)

Answer 1

1) (m+4n)² = m²+8mn+16n²
2) (2a-3b)²= 4a²-12ab+9b²

Answer 2

Simplifying Expressions

Let's simplify the given expressions one by one:

1. (m + 4n)^2 = 8x^3 + 1:

To simplify this expression, we can expand the square of the binomial and equate it to the given expression.

Expanding the square of the binomial (m + 4n)^2, we get:

(m + 4n)^2 = m^2 + 2mn + 16n^2

Now, we can equate this to the given expression:

m^2 + 2mn + 16n^2 = 8x^3 + 1

Unfortunately, the given expression does not provide any information about the values of m, n, or x. Therefore, we cannot simplify it further without additional information.

2. (2a - 3b)^2:

To simplify this expression, we can expand the square of the binomial (2a - 3b)^2:

(2a - 3b)^2 = (2a)^2 - 2(2a)(3b) + (3b)^2 = 4a^2 - 12ab + 9b^2

So, the simplified form of (2a - 3b)^2 is 4a^2 - 12ab + 9b^2.

Please note that without specific values for a and b, we cannot simplify it further.

System of Equations

The given expression "3x1 + x2 + x3 = 2, 2x1 + x2 + 2x3 = 0, x1 + 2x2 + 3x3 = 1" represents a system of equations with three variables (x1, x2, x3).

To solve this system of equations, we can use various methods such as substitution, elimination, or matrix methods. Let's solve it using the elimination method:

1. Multiply the first equation by 2 and the second equation by -3 to eliminate x1: - 6x1 - 2x2 - 2x3 = 4 - -6x1 - 3x2 - 6x3 = 0

2. Add the two equations to eliminate x1: - 6x1 - 2x2 - 2x3 + (-6x1 - 3x2 - 6x3) = 4 + 0 - -5x2 - 8x3 = 4

3. Multiply the first equation by -1 and the third equation by 3 to eliminate x1: -x1 - 2x2 - 3x3 = -1 -3x1 - 6x2 - 9x3 = 3

4. Add the two equations to eliminate x1: -x1 - 2x2 - 3x3 + (-3x1 - 6x2 - 9x3) = -1 + 3 -8x2 - 12x3 = 2

Now, we have two equations: - -5x2 - 8x3 = 4 - -8x2 - 12x3 = 2

We can solve this system of equations to find the values of x2 and x3. However, without additional information or specific values for x2 and x3, we cannot determine their exact values.

Please provide more information or specific values if you would like a more detailed solution.

I hope this helps! Let me know if you have any further questions.