Step 1

Given expression is

\(\displaystyle{\left({3}{x}+{2}\right)}{\left({x}-{5}\right)}{\left({5}{x}+{4}\right)}\)

It is known that

(a+b)(c+d)=a(c+d)+b(c+d)

=ac+ad+bc+bd

Step 2

(3x+2)(x-5)(5x+4)=(3x+2)[(x-5)(5x+4)]

=(3x+2)[x(5x+4)-5(5x+4)]

\(\displaystyle={\left({3}{x}+{2}\right)}{\left[{5}{x}^{{{2}}}+{4}{x}-{25}{x}-{20}\right]}\)

\(\displaystyle={\left({3}{x}+{2}\right)}{\left[{5}{x}^{{{2}}}-{21}{x}-{20}\right]}\)

\(\displaystyle={3}{x}{\left[{5}{x}^{{{2}}}-{21}{x}-{20}\right]}+{2}{\left[{5}{x}^{{{2}}}-{21}{x}-{20}\right]}\)

\(\displaystyle={15}{x}^{{{3}}}-{63}{x}^{{{2}}}-{60}{x}+{10}{x}^{{{2}}}-{42}{x}-{40}\)

\(\displaystyle={15}{x}^{{{3}}}-{53}{x}^{{{2}}}-{102}{x}-{40}\)

Hence,

\(\displaystyle{\left({3}{x}+{2}\right)}{\left({x}-{5}\right)}{\left({5}{x}+{4}\right)}={15}{x}^{{{3}}}-{53}{x}^{{{2}}}-{102}{x}-{40}\)

Given expression is

\(\displaystyle{\left({3}{x}+{2}\right)}{\left({x}-{5}\right)}{\left({5}{x}+{4}\right)}\)

It is known that

(a+b)(c+d)=a(c+d)+b(c+d)

=ac+ad+bc+bd

Step 2

(3x+2)(x-5)(5x+4)=(3x+2)[(x-5)(5x+4)]

=(3x+2)[x(5x+4)-5(5x+4)]

\(\displaystyle={\left({3}{x}+{2}\right)}{\left[{5}{x}^{{{2}}}+{4}{x}-{25}{x}-{20}\right]}\)

\(\displaystyle={\left({3}{x}+{2}\right)}{\left[{5}{x}^{{{2}}}-{21}{x}-{20}\right]}\)

\(\displaystyle={3}{x}{\left[{5}{x}^{{{2}}}-{21}{x}-{20}\right]}+{2}{\left[{5}{x}^{{{2}}}-{21}{x}-{20}\right]}\)

\(\displaystyle={15}{x}^{{{3}}}-{63}{x}^{{{2}}}-{60}{x}+{10}{x}^{{{2}}}-{42}{x}-{40}\)

\(\displaystyle={15}{x}^{{{3}}}-{53}{x}^{{{2}}}-{102}{x}-{40}\)

Hence,

\(\displaystyle{\left({3}{x}+{2}\right)}{\left({x}-{5}\right)}{\left({5}{x}+{4}\right)}={15}{x}^{{{3}}}-{53}{x}^{{{2}}}-{102}{x}-{40}\)