Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[({x}^{2}+3x+x+3)(x-4)(x-6)+24\]
Expand by distributing sum groups.
\[({x}^{2}(x-4)+3x(x-4)+x(x-4)+3(x-4))(x-6)+24\]
Expand by distributing sum groups.
\[{x}^{2}(x-4)(x-6)+3x(x-4)(x-6)+x(x-4)(x-6)+3(x-4)(x-6)+24\]
Expand by distributing terms.
\[({x}^{3}-4{x}^{2})(x-6)+3x(x-4)(x-6)+x(x-4)(x-6)+3(x-4)(x-6)+24\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[{x}^{4}-6{x}^{3}-4{x}^{3}+24{x}^{2}+3x(x-4)(x-6)+x(x-4)(x-6)+3(x-4)(x-6)+24\]
Expand by distributing terms.
\[{x}^{4}-6{x}^{3}-4{x}^{3}+24{x}^{2}+(3{x}^{2}-12x)(x-6)+x(x-4)(x-6)+3(x-4)(x-6)+24\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[{x}^{4}-6{x}^{3}-4{x}^{3}+24{x}^{2}+3{x}^{3}-18{x}^{2}-12{x}^{2}+72x+x(x-4)(x-6)+3(x-4)(x-6)+24\]
Expand by distributing terms.
\[{x}^{4}-6{x}^{3}-4{x}^{3}+24{x}^{2}+3{x}^{3}-18{x}^{2}-12{x}^{2}+72x+({x}^{2}-4x)(x-6)+3(x-4)(x-6)+24\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[{x}^{4}-6{x}^{3}-4{x}^{3}+24{x}^{2}+3{x}^{3}-18{x}^{2}-12{x}^{2}+72x+{x}^{3}-6{x}^{2}-4{x}^{2}+24x+3(x-4)(x-6)+24\]
Expand by distributing terms.
\[{x}^{4}-6{x}^{3}-4{x}^{3}+24{x}^{2}+3{x}^{3}-18{x}^{2}-12{x}^{2}+72x+{x}^{3}-6{x}^{2}-4{x}^{2}+24x+(3x-12)(x-6)+24\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[{x}^{4}-6{x}^{3}-4{x}^{3}+24{x}^{2}+3{x}^{3}-18{x}^{2}-12{x}^{2}+72x+{x}^{3}-6{x}^{2}-4{x}^{2}+24x+3{x}^{2}-18x-12x+72+24\]
Collect like terms.
\[{x}^{4}+(-6{x}^{3}-4{x}^{3}+3{x}^{3}+{x}^{3})+(24{x}^{2}-18{x}^{2}-12{x}^{2}-6{x}^{2}-4{x}^{2}+3{x}^{2})+(72x+24x-18x-12x)+(72+24)\]
Simplify.
\[{x}^{4}-6{x}^{3}-13{x}^{2}+66x+96\]
x^4-6*x^3-13*x^2+66*x+96
