Question

15) y ^ (k + 1) * (2y ^ (2k - 1) + 5y ^ (3 - k)) 4)2y^ 3 . (y ^ (m + 2) - 3y ^ (n + 1)) 16 )2x^ k-2 . (x ^ (2k + 2) + 3x ^ (5 - 2k)) 13)x^ 2 . (2x ^ (m - 2) - x ^ (n + 1))

Answer 1

15: \(y^{k+1}\cdot\left(2y^{2k-1}+5\cdot y^{3-k}\right)\)

\(=y^{k+1}\cdot2\cdot y^{2k-1}+y^{k+1}\cdot5\cdot y^{3-k}\)

\(=2\cdot y^{3k}+5\cdot y^4\)

4: \(2y^3\cdot\left(y^{m+2}-3y^{n+1}\right)\)

\(=2\cdot y^3\cdot y^{m+2}-2y^3\cdot3\cdot y^{n+1}\)

\(=2\cdot y^{m+5}-6\cdot y^{n+4}\)

16: \(2x^{k-2}\cdot\left(x^{2k+2}+3\cdot x^{5-2k}\right)\)

\(=2x^{k-2}\cdot x^{2k+2}+2\cdot x^{k-2}\cdot3\cdot x^{5-2k}=2\cdot x^{3k}+6\cdot x^{3-k}\)

13: \(x^2\cdot\left(2x^{m-2}-x^{n+1}\right)\)

\(=x^2\cdot2\cdot x^{m-2}-x^2\cdot x^{n+1}\)

\(=2\cdot x^{m}-x^{n+3}\)