Question

Как возвести трехчлен в квадрат? как возвести трехчлен (x^2+3x+1) в квадрат?

Answer 1

(a+b+c)^2 = a^2+b^2+c^2+2ab+2ac+2bc
(x^2+3x+1)^2=x^4+9x^2+1+6x^3+2x^2+6x=x^4+6x^3+11x^2+6x+1

Answer 2

How to Square a Trinomial?

To square a trinomial, you need to multiply it by itself. Let's take the trinomial x^2 + 3x + 1 as an example.

To square the trinomial x^2 + 3x + 1, you can use the distributive property and multiply each term by itself and then combine like terms.

Here's the step-by-step process:

1. Square the first term: (x^2)^2 = x^4. 2. Multiply the first and second terms: (x^2)(3x) = 3x^3. 3. Multiply the first and third terms: (x^2)(1) = x^2. 4. Multiply the second term and the first term: (3x)(x^2) = 3x^3. 5. Square the second term: (3x)^2 = 9x^2. 6. Multiply the second and third terms: (3x)(1) = 3x. 7. Multiply the third term and the first term: (1)(x^2) = x^2. 8. Multiply the third term and the second term: (1)(3x) = 3x. 9. Square the third term: (1)^2 = 1.

Now, combine all the terms:

x^4 + 3x^3 + x^2 + 3x^3 + 9x^2 + 3x + x^2 + 3x + 1

Simplifying the expression, we get:

x^4 + 6x^3 + 11x^2 + 6x + 1

So, the square of the trinomial x^2 + 3x + 1 is **x^4 + 6x^3 + 11x^2 + 6x + 1.

Please let me know if you need any further assistance!