Question

# ( P=left[begin{array}{lll}1 & 2 & 3 0 & 5 & 7 0 & 8 & 0end{array}right] Q=left[begin{array}{lll}2 & 0 & 3 3 & 0 & 5 5 & 7 & 0end{array}right] ) then find ( 2 P-3 Q )

Solution

( (9+b)^{3}-3 a^{2} b(a+b) )

( (a+b)left[a^{2}+b^{2}+2 a b-3 a^{2} bright] ) ( (a+b)left[left(a^{2}+bright)^{2}-(a sqrt{3} b)^{2}right] ) ( (a+b)[(a+b+a sqrt{3 b})(a+b-a sqrt{3 b})] )

( 2 P=left[begin{array}{lll}2 & 4 & 6 0 & 10 & 14 0 & 16 & 0end{array}right] quad begin{array}{l}text { Multiplying all element by 2 } text { } text { } end{array} ) ( 3 Q=left(begin{array}{ccc}6 & 0 & 9 9 & 0 & 15 15 & 21 & 0end{array}right) quad ) multiplying by 3

( P-3 P=left[begin{array}{ccc}2-4 & +-0 & 6-9 0-9 & 10-0 & 14-15 0-15 & 16-21 & 0-0end{array}right] )

( left[begin{array}{ccc}-2 & 4 & -3 -9 & 10 & -1 -15 text { } & 5 & text { }end{array}right] )