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Q3. Find the value of each of the following without calculating squares.

(i) [tex]27^2 - 26^2[/tex]

(ii) [tex]118^2 - 117^2[/tex]

Sagot :

GinnyAnswer
To solve the problems [tex]\(27^2-26^2\)[/tex] and [tex]\(118^2-117^2\)[/tex] without actually calculating the squares, we can use the difference of squares formula. The difference of squares formula states that:

[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]

### Part (i) [tex]\(27^2 - 26^2\)[/tex]

Let's denote [tex]\(a = 27\)[/tex] and [tex]\(b = 26\)[/tex].

Using the formula:

[tex]\[ 27^2 - 26^2 = (27 - 26)(27 + 26) \][/tex]

Now, we calculate the values inside the parentheses:

[tex]\[ 27 - 26 = 1 \][/tex]
[tex]\[ 27 + 26 = 53 \][/tex]

Therefore:

[tex]\[ 27^2 - 26^2 = 1 \times 53 = 53 \][/tex]

So, the value of [tex]\(27^2 - 26^2\)[/tex] is [tex]\(53\)[/tex].

### Part (ii) [tex]\(118^2 - 117^2\)[/tex]

Let's denote [tex]\(a = 118\)[/tex] and [tex]\(b = 117\)[/tex].

Using the formula:

[tex]\[ 118^2 - 117^2 = (118 - 117)(118 + 117) \][/tex]

Now, we calculate the values inside the parentheses:

[tex]\[ 118 - 117 = 1 \][/tex]
[tex]\[ 118 + 117 = 235 \][/tex]

Therefore:

[tex]\[ 118^2 - 117^2 = 1 \times 235 = 235 \][/tex]

So, the value of [tex]\(118^2 - 117^2\)[/tex] is [tex]\(235\)[/tex].

In summary:
(i) [tex]\(27^2 - 26^2 = 53\)[/tex]
(ii) [tex]\(118^2 - 117^2 = 235\)[/tex]
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