Question

2) (m²+n²)³ 3) (2a²+b²)³​

Answer 1

Ответ:

(a²-b²)³=a⁶-3a⁴b²+3a²b⁴-b⁶

Степень многочлена (6; 4+2=6; 2+4=6; 6) равна 6.

(m²+n²)³=m⁶+3m⁴n²+3m²n⁴+n⁶

Степень многочлена (6; 4+2=6; 2+4=6; 6) равна 6.

Answer 2

To expand the given expressions, you can use the binomial expansion formula for the cube of a binomial expression, which is:

$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

Let's apply this formula to your expressions:

1. $(m^2 + n^2)^3$: Using the formula, with $a = m^2$ and $b = n^2$, we get: $(m^2 + n^2)^3 = (m^2)^3 + 3(m^2)^2(n^2) + 3(m^2)(n^2)^2 + (n^2)^3$ Simplify each term: $(m^2)^3 = m^6$ $3(m^2)^2(n^2) = 3m^4n^2$ $3(m^2)(n^2)^2 = 3m^2n^4$ $(n^2)^3 = n^6$

   So, the expanded expression is: $(m^2 + n^2)^3 = m^6 + 3m^4n^2 + 3m^2n^4 + n^6$

2. $(2a^2 + b^2)^3$: Using the formula, with $a = 2a^2$ and $b = b^2$, we get: $(2a^2 + b^2)^3 = (2a^2)^3 + 3(2a^2)^2(b^2) + 3(2a^2)(b^2)^2 + (b^2)^3$ Simplify each term: $(2a^2)^3 = 8a^6$ $3(2a^2)^2(b^2) = 12a^4b^2$ $3(2a^2)(b^2)^2 = 3(2a^2)b^4 = 6a^2b^4$ $(b^2)^3 = b^6$

   So, the expanded expression is: $(2a^2 + b^2)^3 = 8a^6 + 12a^4b^2 + 6a^2b^4 + b^6$

These are the expanded forms of the given expressions.