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Simplify the following expression and evaluate them as directed:
3y(2y-7) - 3(y-4) - 63 for y = -2.

Last updated date: 20th Jun 2024
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Hint: In this question, we will first open the small bracket so that the terms get multiplied, and then in the next step we will arrange the terms according to the degree of the terms and then add or subtract to get the simplified expression and finally put the value to get the required answer.

Complete step-by-step solution:
The given algebraic expression is $3y(2y-7) - 3(y-4) – 63$
To simplify, we will first open the bracket.
So, the given expression can be written as:
$3y(2y-7) - 3(y-4) – 63 =6{y^2} - 21y - 3y + 12 - 63$ ---------(1)
On taking the terms of same power together and then adding them, we get:
$6{y^2} - 24y - 51 = 0$ . -------------(2)
So, this is a simplified form of the given expression. The expression is in terms of variable ’y’. The degree of this expression is 2.
Now, we will find the value of the simplified expression at $y =2$.
Putting y = 2 in equation 2, we get:
$6 \times {(2)^2} - 24 \times 2 - 51$
On further solving the above expression, we get:
$6 \times {(2)^2} - 24 \times 2 - 51 = 6 \times 4 - 48 - 51 = 24 – 99 = -75$
Hence, the value of the given expression at $y =2$ is $-75$.

Note: You should have an idea of BODMAS which is used to simplify the mathematical expression involving different mathematical operators. The different operators are used in according the rule of BODMAS where,
B= Bracket
O= of
D= Division
M= Multiplication
A = addition
S =subtraction