Answer

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**Hint:**To solve these questions, we have to simplify the given expression. For simplifying the given expression open the parenthesis and multiply the terms inside and outside them. After opening the parenthesis, simplify the expression by collecting all the like terms together and then combining them.

**Complete step by step answer:**

The given quadratic polynomial is $18{x^2} + 4 - \left[ {6\left( {{x^2} - 2} \right) + 5} \right]$ and we have to simplify it.

To simplify the given quadratic polynomial, we will first solve the expression inside the parenthesis to get

$\Rightarrow 18{x^2} + 4 - \left[ {6 \times {x^2} - 6 \times 2 + 5} \right]$

Simplifying the expression in the parenthesis further, we get

$\Rightarrow 18{x^2} + 4 - \left[ {6{x^2} - 12 + 5} \right]$

Now finally opening the parentheses and simplifying the polynomial while taking the signs also into consideration, we get

$\Rightarrow 18{x^2} + 4 - 6{x^2} + 12 - 5$

Collecting all the like terms, that is, constants and coefficients of ${x^2}$ and arranging them in the general form of a quadratic polynomial, we get

$\Rightarrow 18{x^2} - 6{x^2} + 4 + 12 - 5$

Now, adding or subtracting all the like terms together by taking their signs into consideration and combining them, we get

$\Rightarrow 12{x^2} + 11$

Therefore, $18{x^2} + 4 - [6({x^2} - 2) + 5] = 12{x^2} + 11$

**Hence on simplifying $18{x^2} + 4 - [6({x^2} - 2) + 5]$ we get $12{x^2} + 11$**

**Additional Information:**

In the given question we were given a quadratic polynomial expression to simplify. A quadratic polynomial is a polynomial of degree $2$ . A general quadratic polynomial has the form $f(x) = {a_0}{x^2} + {a_1}x + {a_2}$ , where ${a_0}$ , ${a_1}$ and ${a_2}$ are real numbers and also ${a_0} \ne 0$ .

Like terms can be defined as those terms in the mathematical expressions whose variables and the exponents are the same.

**Note:**A common mistake while solving these questions occur when students don’t follow the BODMAS rule. If the parenthesis are not opened and solved first, then this can lead to wrong answers. The BODMAS rule states that in a given mathematical expression which has to be simplified the order of precedence of operators should be: Brackets of Division, Multiplication, Addition, and Subtraction.

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