Question

Умножите многочлен на многочлен! 3a(2a^3-5a^2+2) (a+5)(2a-7) (9x+y)(4x-3y) Спасибо огромное заранее!

Answer 1

6а⁴-15а³+6а
2а²+10а-7а-35=2а²+3а-35
36х²+4ху-27ху-12у²=36х²-23ху-12у²

Answer 2

Multiplying Polynomials

To multiply the given polynomials, we'll use the distributive property to expand and simplify each term. Let's start with the given expression:

3a(2a^3-5a^2+2) + (a+5)(2a-7) + (9x+y)(4x-3y)

Step 1: Multiply the First Pair of Polynomials

First, we'll multiply the first pair of polynomials: 3a(2a^3-5a^2+2)

This yields: 6a^4 - 15a^3 + 6a

Step 2: Multiply the Second Pair of Polynomials

Next, we'll multiply the second pair of polynomials: (a+5)(2a-7)

Expanding this expression gives us: 2a^2 - 7a + 10a - 35

Simplifying further, we get: 2a^2 + 3a - 35

Step 3: Multiply the Third Pair of Polynomials

Finally, we'll multiply the third pair of polynomials: (9x+y)(4x-3y)

Expanding this expression yields: 36x^2 - 27xy + 4xy - 3y^2

Simplifying further, we get: 36x^2 - 23xy - 3y^2

Step 4: Combine the Results

Now, we'll combine the results from the three steps: 6a^4 - 15a^3 + 6a + 2a^2 + 3a - 35 + 36x^2 - 23xy - 3y^2

Final Result

Combining like terms, the final result of multiplying the given polynomials is: 6a^4 - 15a^3 + 2a^2 + 6a + 3a - 35 + 36x^2 - 23xy - 3y^2

This is the simplified form of the product of the given polynomials.

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