Question

Разложите на множители (a+3b)^2-(3a-b)^2 преобразуйте алгебраическое выражение в многочлен стандартного вида: 3(2-x)^2-(2x^2+x-5)(x^2-2)+(x^2+4)(4-x^2) помогите пожалуйста, очень срочно надо!

Answer 1

(a+3b)^2-(3a-b)^2=(a+3b-3a+b)(a+3b+3a-b)=(4b-2a)(4a+2b)=4(2b-a)(2a+b)

Answer 2

Factoring and Simplifying Algebraic Expressions

To factor the expression *(a + 3b)^2 - (3a - b)^2* and simplify the algebraic expression *3(2-x)^2 - (2x^2+x-5)(x^2-2) + (x^2+4)(4-x^2)*, we can follow these steps:

1. Factoring the Expression *(a + 3b)^2 - (3a - b)^2*

The expression *(a + 3b)^2 - (3a - b)^2* can be factored using the difference of squares formula, which states that *a^2 - b^2 = (a + b)(a - b)*.

So, we can factor the given expression as follows: *(a + 3b)^2 - (3a - b)^2 = ((a + 3b) + (3a - b))((a + 3b) - (3a - b))*

This simplifies to: *(4a + 2b)(-2a + 4b)*

This is the factored form of the given expression.

Source: 2. Simplifying the Algebraic Expression *3(2-x)^2 - (2x^2+x-5)(x^2-2) + (x^2+4)(4-x^2)*

To simplify the given algebraic expression, we can follow these steps:

- Expand and simplify each term in the expression. - Combine like terms.

The given expression is: *3(2-x)^2 - (2x^2+x-5)(x^2-2) + (x^2+4)(4-x^2)*

First, let's expand each term:

- Expanding *3(2-x)^2* gives us *3(4 - 4x + x^2)* - Expanding *(2x^2+x-5)(x^2-2)* gives us *2x^4 - 4x^2 + x^3 - 2x^2 + 5x - 10* - Expanding *(x^2+4)(4-x^2)* gives us *4x^2 - x^4 + 16 - 4x^2*

Now, let's combine like terms:

- The expression becomes: *12 - 12x + 3x^2 - 2x^4 + x^3 - 2x^2 + 5x - 10 + 4x^2 - x^4 + 16 - 4x^2*

Combining like terms further simplifies the expression to: *-3x^4 + x^3 - 3x^2 - 11x + 18*

This is the simplified form of the given algebraic expression.

Source: I hope this helps! If you have any further questions or need additional assistance, feel free to ask.