Question 145979
I'll do the first two to get you started


# 1




{{{(2x-3)(3x^2+5x-7)}}} Start with the given expression.



{{{2x(3x^2+5x-7)-3(3x^2+5x-7)}}} Expand.



{{{(2x)*(3x^2)+(2x)*(5x)+(2x)*(-7)+(-3)*(3x^2)+(-3)*(5x)+(-3)*(-7)}}} Distribute.



{{{6*x^3+10*x^2-14*x-9*x^2-15*x+21}}} Multiply.



{{{6*x^3+x^2-29*x+21}}} Now combine like terms.



 So {{{(2x-3)(3x^2+5x-7)}}} expands to {{{6*x^3+x^2-29*x+21}}}.



In other words, {{{(2x-3)(3x^2+5x-7)=6*x^3+x^2-29*x+21}}}.




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# 2





{{{(-8ab^5)*(5a^4b)}}} Start with the given expression.



{{{-40ab^5*a^4b}}} Multiply the coefficients {{{-8}}} and {{{5}}} to get {{{-40}}}



{{{-40a^(1+4)b^(5+1)}}} When you multiply monomials, simply add the exponents.



{{{-40a^5b^6}}} Add.



So {{{(-8ab^5)*(5a^4b)=-40a^5b^6}}}.