Question

Simplify $3x\left(4x-5\right)+3$ and find its values for

(i) $x=3$

(ii)$x=\frac{1}{2}$

Answer 1

Step 1: Simplify $3x\left(4x-5\right)+3$.

Simplify $3x\left(4x-5\right)+3$using BODMAS.

$\begin{array}{c}3x(4x-5)+3=(3x\times 4x)-(3x\times 5)+3\\ =12x^2-15x+3\end{array}$

Step 2: Calculate the value of $12x^2-15x+3$at $x=3$.

Apply the value of $12x^2-15x+3$at $x=3$ and solve:

$\begin{array}{c}12x^2-15x+3=12{\left(3\right)}^2-15\left(3\right)+3\\ =(12\times 9)-(15\times 3)+3\\ =108-45+3\\ =111-45\\ =66\end{array}$

Step 3: Calculate the value of $12x^2-15x+3$at $x=\frac{1}{2}$.

Apply the value of $12x^2-15x+3$at $x=\frac{1}{2}$ and solve:

$\begin{array}{c}12x^2-15x+3=12{\left(\frac{1}{2}\right)}^2-15\left(\frac{1}{2}\right)+3\\ =(12\times \frac{1}{4})-(15\times \frac{1}{2})+3\\ =3-7.5+3\\ =6-7.5\\ =-1.5\\ =\frac{-3}{2}\end{array}$

Hence, the simplified form of $3x\left(4x-5\right)+3$ is $12x^2-15x+3$and its value at $x=3$ and $x=\frac{1}{2}$is $66$ and $\frac{-3}{2}$ respectively.