Question

11) (x ^ 2 - 9x + x ^ 3 - 2) .(x-x^ 2 ) 13) ( 1 2 x^ n-2 -x^ 2 ). (4/3 * x ^ 3 + 6x ^ (3 - n)) 12) (2y ^ 3 - 5y + y ^ 4 - 1) .(y-5y) 1)( 1 5 x^ 2k-2 -x^ 2 ). (5/2 * x ^ (- 2k + 3) + 6x ^ (1 - k))

Answer 1

11: \(\left(x^2-9x+x^3-2\right)\left(x-x^2\right)\)

\(=\left(x^3+x^2-9x-2\right)\left(-x^2+x\right)\)

\(=-x^5+x^4-x^4+x^3+9x^3-9x^2+2x^2-2x\)

\(=-x^5+10x^3-7x^2-2x\)

13: \(\left(\frac12x^{n-2}-x^2\right)\cdot\left(\frac43x^3+6x^{3-n}\right)\)

\(=\frac12\cdot x^{n-2}\cdot\frac43\cdot x^3+\frac12\cdot x^{n-2}\cdot6\cdot x^{3-n}-\frac43x^3\cdot x^2-x^2\cdot6\cdot x^{3-n}\)

\(=\frac23x^{n+1}+3x-\frac43x^5-6\cdot x^{5-n}\)

12: \(\left(2y^3-5y+y^4-1\right)\left(y-5y\right)\)

\(=-4y\left(y^4+2y^3-5y-1\right)\)

\(=-4y\cdot y^4-4y\cdot2y^3+4y\cdot5y+4y\cdot1=-4y^5-8y^4+20y^2+4y\)