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Question

Complete the table
first expression second expression product(i)ab+c+d(ii)x+y55xy(iii)p6p27p+5(iv)4p2q2p2q2(v)a+b+cabc

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Solution

(i) Given, a×(b+c+d)=ab+ac+ad
(ii) Given, (x+y5)×5xy=x(5xy)+y(5xy)5(5xy)
=5x2y+5xy225xy
(iii) p×(6p27p+5)=p(6p2)p(7p)+p(5)
=6p37p2+5p
(iv) Given 4p2q2(p2q2)=4p2q2(p2)4p2q2(q2)
4p2+2q24p2q2+2 (Since, when the bases are same then exponents will be added)
=4p4q24p2q4
(v) Given (a+b+c)×abc=a(abc)+b(abc)+c(abc)
=a2bc+ab2c+abc2
Thus, the table can be completed as follows.
first expression second expression product(i)ab+c+dab+ac+ad(ii)x+y55xy5x2y+5xy225xy(iii)p6p27p+56p37p2+5p(iv)4p2q2p2q24p4q24p2q4(v)a+b+cabca2bc+ab2c+abc2


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