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Find the values of the following expressions if $a = 4$ and $b = -1$ - Junior Cycle Mathematics - Question 9 - 2012

Question 9

Find the values of the following expressions if $a = 4$ and $b = -1$. (i) $2a + 3b - 2 = $ (ii) $a^2 + b^2 + 4 = $ (iii) $\frac{a + 2b}{2} = $ (b) Multiply $x + ... show full transcript

Worked Solution & Example Answer:Find the values of the following expressions if $a = 4$ and $b = -1$ - Junior Cycle Mathematics - Question 9 - 2012

Step 1

(i) $2a + 3b - 2 = $

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Answer

First, substitute the values of $a$ and $b$ :

$2(4) + 3(-1) - 2 = 8 - 3 - 2 = 3$

Thus, the answer is: $3$ .

Step 2

(ii) $a^2 + b^2 + 4 = $

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Answer

Now, substitute again:

$4^2 + (-1)^2 + 4 = 16 + 1 + 4 = 21$

The result is: $21$ .

Step 3

(iii) $\frac{a + 2b}{2} = $

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Answer

Substituting the values:

$\frac{4 + 2(-1)}{2} = \frac{4 - 2}{2} = \frac{2}{2} = 1$

Thus, the answer is: $1$ .

Step 4

(b) Multiply $x + 4$ by $x - 6$.

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Answer

Using the distributive property:

$(x + 4)(x - 6) = x(x - 6) + 4(x - 6)$

Expanding both terms:

$= x^2 - 6x + 4x - 24$

Combining like terms gives:

$= x^2 - 2x - 24$

Thus, the result is: $x^2 - 2x - 24$ .

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