Question

(a) Simplify 3x (4x – 5) + 3 and find its values for (i) x = 3 (ii) x =\(\frac{1}{2}\)
(b) Simplify a (a²+ a + 1) + 5 and find its value for (i) a = 0, (ii) a = 1 (iii) a = – 1.

Answer 1

(a) 3x (4x – 5) + 3
=3x ( 4x) – 3x( 5) +3
=12x² – 15x + 3

(i) Putting x=3 in the equation we get 
12x² – 15x + 3 
=12(3²) – 15 (3) +3
= 108 – 45 + 3
= 66

(ii) Putting x=\(\frac{1}{2}\) in the equation we get
12x² – 15x + 3 

= 12 (\(\frac{1}{2}\))² – 15 (\(\frac{1}{2}\)) + 3

= 12 (\(\frac{1}{4}\)) – \(\frac{15}{2}\) +3

= 3 – \(\frac{15}{2}\) + 3

= 6- \(\frac{15}{2}\)

= \(\frac{(12- 15 ) }{2}\)

=\(\frac{ -3}{2}\)

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(b) a (a² +a +1) +5
= a \(\times\) a² + a \(\times\) a + a \(\times\) 1 + 5
 =a³+a²+a+ 5

(i) putting a=0 in the equation we get 0³+0²+0+5=5

(ii) putting a=1 in the equation we get 1³ + 1² + 1+5 = 1 + 1 + 1+5 = 8

(iii) Putting a = -1 in the equation we get (-1)³+(-1)² + (-1) +5 = -1 + 1 – 1+5 = 4