Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[({k}^{2}-3k+2k-6)(k+5)(k+10)+375\]
Expand by distributing sum groups.
\[({k}^{2}(k+5)-3k(k+5)+2k(k+5)-6(k+5))(k+10)+375\]
Expand by distributing sum groups.
\[{k}^{2}(k+5)(k+10)-3k(k+5)(k+10)+2k(k+5)(k+10)-6(k+5)(k+10)+375\]
Expand by distributing terms.
\[({k}^{3}+5{k}^{2})(k+10)-3k(k+5)(k+10)+2k(k+5)(k+10)-6(k+5)(k+10)+375\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[{k}^{4}+10{k}^{3}+5{k}^{3}+50{k}^{2}-3k(k+5)(k+10)+2k(k+5)(k+10)-6(k+5)(k+10)+375\]
Expand by distributing terms.
\[{k}^{4}+10{k}^{3}+5{k}^{3}+50{k}^{2}-(3{k}^{2}+15k)(k+10)+2k(k+5)(k+10)-6(k+5)(k+10)+375\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[{k}^{4}+10{k}^{3}+5{k}^{3}+50{k}^{2}-(3{k}^{3}+30{k}^{2}+15{k}^{2}+150k)+2k(k+5)(k+10)-6(k+5)(k+10)+375\]
Expand by distributing terms.
\[{k}^{4}+10{k}^{3}+5{k}^{3}+50{k}^{2}-(3{k}^{3}+30{k}^{2}+15{k}^{2}+150k)+(2{k}^{2}+10k)(k+10)-6(k+5)(k+10)+375\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[{k}^{4}+10{k}^{3}+5{k}^{3}+50{k}^{2}-(3{k}^{3}+30{k}^{2}+15{k}^{2}+150k)+2{k}^{3}+20{k}^{2}+10{k}^{2}+100k-6(k+5)(k+10)+375\]
Expand by distributing terms.
\[{k}^{4}+10{k}^{3}+5{k}^{3}+50{k}^{2}-(3{k}^{3}+30{k}^{2}+15{k}^{2}+150k)+2{k}^{3}+20{k}^{2}+10{k}^{2}+100k-(6k+30)(k+10)+375\]
Use the FOIL method: \((a+b)(c+d)=ac+ad+bc+bd\).
\[{k}^{4}+10{k}^{3}+5{k}^{3}+50{k}^{2}-(3{k}^{3}+30{k}^{2}+15{k}^{2}+150k)+2{k}^{3}+20{k}^{2}+10{k}^{2}+100k-(6{k}^{2}+60k+30k+300)+375\]
Remove parentheses.
\[{k}^{4}+10{k}^{3}+5{k}^{3}+50{k}^{2}-3{k}^{3}-30{k}^{2}-15{k}^{2}-150k+2{k}^{3}+20{k}^{2}+10{k}^{2}+100k-6{k}^{2}-60k-30k-300+375\]
Collect like terms.
\[{k}^{4}+(10{k}^{3}+5{k}^{3}-3{k}^{3}+2{k}^{3})+(50{k}^{2}-30{k}^{2}-15{k}^{2}+20{k}^{2}+10{k}^{2}-6{k}^{2})+(-150k+100k-60k-30k)+(-300+375)\]
Simplify.
\[{k}^{4}+14{k}^{3}+29{k}^{2}-140k+75\]
k^4+14*k^3+29*k^2-140*k+75
