Question

Преобразуйтe выражение в многочлен1. (x^2+3y)^22.(0,3a^2+4b)^23.(0,5m^2-5n)^2

Answer 1

Х^4+6ху+9у^2
0,09а^4+2,4ав+16в^2
0,25м^4-5mn+5n^2

Answer 2

1. (x^2+3y)^2: Expanding the expression using the binomial theorem, we have:

(x^2+3y)^2 = (x^2)^2 + 2(x^2)(3y) + (3y)^2 = x^4 + 6xy + 9y^2

Therefore, the expression (x^2+3y)^2 can be simplified to the polynomial x^4 + 6xy + 9y^2.

2. (0,3a^2+4b)^2: Expanding the expression using the binomial theorem, we have:

(0,3a^2+4b)^2 = (0,3a^2)^2 + 2(0,3a^2)(4b) + (4b)^2 = 0,09a^4 + 0,24a^2b + 16b^2

Therefore, the expression (0,3a^2+4b)^2 can be simplified to the polynomial 0,09a^4 + 0,24a^2b + 16b^2.

3. (0,5m^2-5n)^2: Expanding the expression using the binomial theorem, we have:

(0,5m^2-5n)^2 = (0,5m^2)^2 - 2(0,5m^2)(5n) + (5n)^2 = 0,25m^4 - 5m^2n + 25n^2

Therefore, the expression (0,5m^2-5n)^2 can be simplified to the polynomial 0,25m^4 - 5m^2n + 25n^2.