Question

Write the expansion of (– m + n)2​

Answer 1

Answer:

nitrogen (N2) ................

Answer 2

Answer:

Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n=n∑k=0nCk⋅(an−kbk)(a+b)n=∑k=0n⁡nCk⋅(an-kbk).

2∑k=02!(2−k)!k!⋅(m)2−k⋅(n)k∑k=02⁡2!(2-k)!k!⋅(m)2-k⋅(n)k

Expand the summation.

2!(2−0)!0!(m)2−0⋅(n)0+2!(2−1)!1!(m)2−1⋅(n)+2!(2−2)!2!(m)2−2⋅(n)22!(2-0)!0!(m)2-0⋅(n)0+2!(2-1)!1!(m)2-1⋅(n)+2!(2-2)!2!(m)2-2⋅(n)2

Simplify the exponents for each term of the expansion.

1⋅(m)2⋅(n)0+2⋅(m)⋅(n)+1⋅(m)0⋅(n)21⋅(m)2⋅(n)0+2⋅(m)⋅(n)+1⋅(m)0⋅(n)2

Simplify each term.

m2+2mn+n2m2+2mn+n2

(m+n)2(m+n)2