question_answer

(a) Simplify : \[3x\left( 4x-5 \right)+3\]and find its value

(i) x = 3 (ii) x = \[\frac{1}{2}\]:

(b) Simplify: \[a\left( {{a}^{2}}+a+1 \right)+5\]and find its value for (a) a = 0 (b) a = 1 (c) \[a\text{ }=-1.\]

Answer:

(a) \[3x\text{ }\left( 4x5 \right)+3\]

\[=12{{x}^{2}}15x+3\]

For x = 3, \[=12{{\left( 3 \right)}^{2}}15\left( 3 \right)+3\]

\[=12\left( 9 \right)45+3\]

\[=10845+3=66\]

For x =\[\frac{1}{2}\]      \[=12{{\left( \frac{1}{2} \right)}^{2}}-15\left( \frac{1}{2} \right)+3\]

\[=3-\frac{15}{2}+3\]

\[=6-\frac{15}{2}\]

\[=\frac{12-15}{2}=\frac{-3}{2}\]

(b) \[a\left( {{a}^{2}}+a+1 \right)+5=\left( a\times {{a}^{2}} \right)+\left( a\times a \right)+\left( a\times 1 \right)+5\]

\[={{a}^{3}}+\text{ }{{a}^{2}}+\text{ }a+5\]

For a = 0  \[=\text{ }{{\left( 0 \right)}^{3}}+{{\left( 0 \right)}^{2}}+\left( 0 \right)+5\]

= 5

For a = 1 \[{{\left( 1 \right)}^{3}}+{{\left( 1 \right)}^{2}}+\left( 1 \right)+5\]

\[=1+1+1+5\]

= 8

For\[a\text{ }=1\] \[{{\left( 1 \right)}^{3}}+{{\left( 1 \right)}^{2}}+\left( 1 \right)+5\]

\[=\text{ }1+11+5\]

= 4