Answer :

Here we have the First and Second expressions as 5q and p + q-2r respectively.

The process involved in the multiplication is :

Step1.Write the product of the expressions using multiplication symbol: 5q×(p + q-2r)

Step2.**Use distributive law** :Multiply the monomial by the first term of the polynomial then multiply the monomial by the second term and then multiply the monomial by the third term of the polynomial and add their products: 5pq + 5q^{2}-10qr

Step3.Simplify the terms: 5q^{2} + 5pq-10qr

2. Similarly ,following the above process we calculate

(kl + lm + mn)(3k)

= (3k)(kl) + (3k)(lm) + (3k)(mn)

= 3k^{2}l + 3klm + 3kmn

3. Similarly ,following the above process we calculate

(ab^{2})( a + b^{2} + c^{3}) = ab^{2}(a) + ab^{2} (b^{2}) + ab^{2}(c^{3}) = a^{2}b^{2} + ab^{4} + ab^{2}c^{3}

4.Similarly ,following the above process we calculate

(x-2y + 3z)(xyz) = ( x-2y + 3z)×(xyz) = x^{2}yz-2xy^{2}z + 3xyz^{2}

5. Similarly ,following the above process we calculate

(a^{2}bc + b^{2}cd-abd^{2})(a^{2}b^{2}c^{2}) = (a^{2}bc + b^{2}cd- abd^{2})×(a^{2}b^{2}c^{2}) = a^{4}b^{3}c^{3} + a^{2}b^{4}c^{3}d-a^{3}b^{3}c^{2}d^{2}

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