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We appreciate your visit to You are told that tex 137 2 18769 tex Use this fact and the idea above to work out the value of tex 133 times. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

You are told that [tex]$137^2 = 18769$[/tex].

Use this fact and the idea above to work out the value of [tex]$133 \times 141$[/tex].

(Note: Do not multiply 133 by 141 directly.)

Answer :

We start with the observation that
[tex]$$
133 = 137 - 4 \quad \text{and} \quad 141 = 137 + 4.
$$[/tex]

This suggests using the difference of squares formula, which states that for any numbers [tex]$a$[/tex] and [tex]$b$[/tex],
[tex]$$
(a-b)(a+b) = a^2 - b^2.
$$[/tex]

Here, let [tex]$a = 137$[/tex] and [tex]$b = 4$[/tex]. Then,
[tex]$$
133 \times 141 = (137-4)(137+4) = 137^2 - 4^2.
$$[/tex]

We are given that:
[tex]$$
137^2 = 18769.
$$[/tex]

And we calculate:
[tex]$$
4^2 = 16.
$$[/tex]

Substitute these values into the expression:
[tex]$$
133 \times 141 = 18769 - 16 = 18753.
$$[/tex]

Thus, the value of [tex]$133 \times 141$[/tex] is [tex]$\boxed{18753}$[/tex].

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