Question

Подайте у вигляді многочлена стандартного вигляду вираз: 4х(х2+3х – 2); (х – 1)(х + 5); (5m – 2n)(3m + n).​

Answer 1

Ответ:

1) 4x•(x•2+3x-2)

4x•(2x+3x-2)

4x•(5x-2)

20x²-8x

2) (x-1)•(x+5)

x•x+5x-x-5

x²+5x-x-5

x²+4x-6

3) (5m – 2n)(3m + n)

5m•3m+5mn-2n•3m-2n•n

15m²+5mn-6mn-2n²

15m²-mn-2n²

Answer 2

1. 4x(x^2 + 3x - 2): The expression can be expanded as follows: 4x(x^2 + 3x - 2) = 4x * x^2 + 4x * 3x - 4x * 2 = 4x^3 + 12x^2 - 8x

Therefore, the expression 4x(x^2 + 3x - 2) can be written in standard form as 4x^3 + 12x^2 - 8x.

2. (x - 1)(x + 5): Using the FOIL method (First, Outer, Inner, Last), we can expand the expression: (x - 1)(x + 5) = x * x + x * 5 - 1 * x - 1 * 5 = x^2 + 5x - x - 5 = x^2 + 4x - 5

Therefore, the expression (x - 1)(x + 5) can be written in standard form as x^2 + 4x - 5.

3. (5m - 2n)(3m + n): Using the FOIL method, we can expand the expression: (5m - 2n)(3m + n) = (5m * 3m) + (5m * n) + (-2n * 3m) + (-2n * n) = 15m^2 + 5mn - 6mn - 2n^2 = 15m^2 - mn - 2n^2

Therefore, the expression (5m - 2n)(3m + n) can be written in standard form as 15m^2 - mn - 2n^2.