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Algebraic Expressions and Identities

Short Answer Type

51.

Fint the product.

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52.

Fint the product.

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53.

Find the product.

X x X²x X³x X⁴

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54.
Simplify 3x(4x - 5) + 3 and find its values for (i) x = 3 (ii) $space space space space space space space space straight x space equals space 1 half$

3x(4x - 5) + 3 = 3x X 4x + 3x X (-5) + 3
                    = (3 x 4) x X x X +3 X (-5) X x +3
                    = 12 X x²+ (-15) x X +3
                    = 12x²- 15x + 3

(i) For x = 3 , 12x²- 15x + 3 = 12(3)²- 15(3) + 3
                                         = 12 x 9 - 45 + 3
                                         = 111 - 45 = 66

(ii) For $space space space space space space straight x equals 1 half$ , 12x²- 15x + 3   = $space space space space space space space space space space space 12 open parentheses 1 half close parentheses squared minus 15 open parentheses 1 half close parentheses plus 3$

                                                 =   $space space space space space space space space space space space 12 open parentheses 1 fourth close parentheses minus 15 over 2 plus 3$

                                                 = $space space space 3 minus 15 over 2 plus 3 equals 6 minus 15 over 2 space space$

                                                 = $space space space space space space space space space space space space space fraction numerator 12 minus 15 over denominator 2 end fraction equals fraction numerator negative 3 over denominator 2 end fraction$