How do you simplify this?[tex](9k^{6}+8k^{4}-6k^{2})(4k^{2}-5)[/tex]

ANSWER[tex]36k^{8} -13{k}^{6} -64k^{4} + 30 {k}^{2} [/tex]EXPLANATIONRecall the distributive property:[tex](a + b + c)(d + e) = a(d + e) + b(d + e) + c(d + e)[/tex]We apply this property multiple times to simplify[tex](9k^{6}+8k^{4}-6k^{2})(4k^{2}-5)[/tex]This implies that:[tex]9k^{6}(4k^{2}-5)+8k^{4}(4k^{2}-5)-6k^{2}(4k^{2}-5)[/tex]We apply the distributive property again:This time: a(b+c)=ac+ab[tex] \implies \: 9k^{6} \times 4k^{2}-5 \times 9 {k}^{6} +8k^{4} \times 4k^{2}-5 \times 8 {k}^{4} -6k^{2} \times 4k^{2} + 5 \times 6 {k}^{2} [/tex][tex]\implies \: 36k^{8} -45{k}^{6} +32k^{6} -40 {k}^{4} -24k^{4} + 30 {k}^{2} [/tex][tex]\implies 36k^{8} -13{k}^{6} -64k^{4} + 30 {k}^{2} [/tex]NB: [tex]k^{n}\times{k}^{m}=k^{m+n} [/tex]