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Algebraic Expressions and Identities

Short Answer Type

31.

Find the product of the following pairs of monomials.
4p, 0

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32.
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
(p, q); (10m, 5n); (20x², 5y²); (4x, 3x²); (3mn, 4np)

(i)    $open space space space space space space space space table attributes columnalign right end attributes row cell Length space equals space straight p end cell row cell Breadth space equals space straight q end cell end table close curly brackets$         ∴   Area of the rectang
                                             = p x q = pq

(ii) $space space space space space space space space space space space open space space table attributes columnalign right end attributes row cell Length space equals space 10 straight m end cell row cell Breadth space equals space 5 straight n end cell end table close curly brackets$ ∴ Area = 10m x 5n
   = 10 x 5 x m x n
   = 50mn

(iii) $space space space space space space space open table attributes columnalign right end attributes row cell Length space equals space 20 straight x squared end cell row cell Breadth space equals space 5 straight y squared end cell end table close curly brackets$     ∴ Area = 20x² x 5y² = 20 x 5 x x² x y²
                                                                   = 100x²y²


(iv) $space space space space space space space space space space space space space open table attributes columnalign right end attributes row cell Length space equals space 4 straight x end cell row cell Breadth space equals space 3 straight x squared end cell end table close curly brackets$              ∴    Area = 4x x 3 x x²
                                                                 = 4 x 3 x x²
                                                                      = 12x³

(v)     $space space space space space space open table attributes columnalign right end attributes row cell Length space equals space 3 mn end cell row cell Breadth space equals space 4 np end cell end table close curly brackets$                ∴   Area = 3mn x 4np
= (3 x 4) x m x n x n xp
= 12 mn²p