Add $2 a + 3 b + c + d, - a + b - c - d$ and $3 a - 4 b - 2 c - 2 d$ . Find the value of the final expression if a=2, b=3, c=4, d=5. [3 MARKS]

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Solution

Forming the equation: 1 Mark
Sum: 1 Mark
Value: 1 Mark

We have to find the sum of the expressions
$2 a + 3 b + c + d, - a + b - c - d$
and $3 a - 4 b - 2 c - 2 d$ .

$(2 a + 3 b + c + d) + (- a + b - c - d) + (3 a - 4 b - 2 c - 2 d)$

$2 a + 3 b + c + d - a + b - c - d + 3 a - 4 b - 2 c - 2 d$

$2 a - a + 3 a + 3 b + b - 4 b + c - c - 2 c + d - d - 2 d$

$4 a + 0 \times b - 2 c - 2 d$

Sum $= 4 a - 2 c - 2 d$
As per question ,
a = 2, b = 3, c = 4, d = 5
So, on substituting the values we get,
Sum = $4 \times 2 - 2 \times 4 - 2 \times 5$
= $8 - 8 - 10$
= $- 10$
The value of the expression is $- 10$ .

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