Question

Умножить многочлены: (a+3) (a-7) (x-5) (x²+4) (3a²-8) (a²-3a+1) 5x*(x-4) (x+6) (x+1) (3x²-4x+10)

Answer 1

(а+3)(а-7)=а^2 - 7a +3a - 21 =  а^2 - 4a - 21

(x-5)(x^2 +4)=x^3 + 4x - 5x^2 - 20

(3a^2-8) ( a^2-3a+1)=3a^4 + 24a -8 -9a^3 + 3a^2

5x(x-4)(x+6) = 5x(x^2 + 2x - 24)= 5x^3 + 10x^2 - 120x

(x+1)(3x^2 - 4x +10)= 3x^3- 4x^2 +10x +3x^2 - 4x+10 

Answer 2

To multiply these polynomials, we can use the distributive property and combine like terms. It will be a long process, so let's break it down into steps:

Step 1: Multiply the first three binomials (a+3) (a-7) (x-5) = (a²-4a-21) (x-5)

Step 2: Multiply the next two binomials (x²+4) (3a²-8) = 3a²x²-8x²+12a²-32

Step 3: Multiply the last three binomials (a²-3a+1) 5x*(x-4) (x+6) = 5a²x³-65a²x²+227a²x-215a²-75ax³+855ax²-2745ax+2260x³-3350x²+1470x

Step 4: Multiply the last binomial with the previous result (3x²-4x+10) (5a²x³-65a²x²+227a²x-215a²-75ax³+855ax²-2745ax+2260x³-3350x²+1470x) = 15a²x⁵-175a²x⁴+748a²x³-12140a²x²+35420a²x-22540a²-225ax⁴+2475ax³-10725ax²+17685ax -20250x³+34250x²-13650x+14700

Step 5: Combine like terms to simplify the expression 15a²x⁵-175a²x⁴-210ax⁴+748a²x³+2475ax³-12140a²x²-10725ax²+35420a²x-22540a² -20250x³+34250x²-13650x+14700

Therefore, the product of the given polynomials is 15a²x⁵-175a²x⁴-210ax⁴+748a²x³+2475ax³-12140a²x²-10725ax²+35420a²x-22540a² -20250x³+34250x²-13650x+14700.