what is the product?\n$(7x^{2})(2x^{3}+5)(x^{2}-4x - 9)$\n$14x^{5}-x^{4}-46x^{3}-58x^{2}-20x…

what is the product?\n$(7x^{2})(2x^{3}+5)(x^{2}-4x - 9)$\n$14x^{5}-x^{4}-46x^{3}-58x^{2}-20x - 45$\n$14x^{6}-56x^{5}-91x^{4}-140x^{3}-315x^{2}$\n$14x^{7}-56x^{6}-126x^{5}+35x^{4}-140x^{3}-315x^{2}$\n$14x^{12}-182x^{6}+35x^{4}-455x^{2}$

what is the product?\n$(7x^{2})(2x^{3}+5)(x^{2}-4x - 9)$\n$14x^{5}-x^{4}-46x^{3}-58x^{2}-20x - 45$\n$14x^{6}-56x^{5}-91x^{4}-140x^{3}-315x^{2}$\n$14x^{7}-56x^{6}-126x^{5}+35x^{4}-140x^{3}-315x^{2}$\n$14x^{12}-182x^{6}+35x^{4}-455x^{2}$

Answer

Explanation:

Step1: Multiply first two polynomials

[ \begin{align*} (7x^{2})(2x^{3}+5)&=7x^{2}\times2x^{3}+7x^{2}\times5\ &=14x^{2 + 3}+35x^{2}\ &=14x^{5}+35x^{2} \end{align*} ]

Step2: Multiply the result by the third polynomial

[ \begin{align*} &(14x^{5}+35x^{2})(x^{2}-4x - 9)\ &=14x^{5}\times x^{2}-14x^{5}\times4x-14x^{5}\times9+35x^{2}\times x^{2}-35x^{2}\times4x-35x^{2}\times9\ &=14x^{5 + 2}-56x^{5+1}-126x^{5}+35x^{2 + 2}-140x^{2+1}-315x^{2}\ &=14x^{7}-56x^{6}-126x^{5}+35x^{4}-140x^{3}-315x^{2} \end{align*} ]

Answer:

14x^{7}-56x^{6}-126x^{5}+35x^{4}-140x^{3}-315x^{2}