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What is the constant term in the expansion of $(x^4+x+5)(x^5+x^3+15)$?

Guest Dec 4, 2014

Best Answer 

 #2
avatar
+5

$$x^4*x^5=x^9$$

$${{\mathtt{x}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}} = {{\mathtt{x}}}^{{\mathtt{7}}}$$

$$x^4*15=15x^4$$

$$x*x^5=x^6$$

$$x*x^3=x^4$$

$$x*15=15x$$

$$5*x^5=5x^5$$

$$5*x^3=5x^3$$

$$5*15=75$$

simplify gives you $$x^9+x^7+x^6+5x^5+16x^4+5x^3+75$$

Guest Dec 4, 2014
 #1
avatar+87301 
+5

The constant term is just the product of the two constant terms in each polynomial....thus 15 * 5 = 75

 

 

CPhill  Dec 4, 2014
 #2
avatar
+5
Best Answer

$$x^4*x^5=x^9$$

$${{\mathtt{x}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{3}}} = {{\mathtt{x}}}^{{\mathtt{7}}}$$

$$x^4*15=15x^4$$

$$x*x^5=x^6$$

$$x*x^3=x^4$$

$$x*15=15x$$

$$5*x^5=5x^5$$

$$5*x^3=5x^3$$

$$5*15=75$$

simplify gives you $$x^9+x^7+x^6+5x^5+16x^4+5x^3+75$$

Guest Dec 4, 2014

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