Look at the pattern2 imes 6-4- 2-43 times 7-5- 2-4 The next lines of the given pattern is equal to

The correct option is A 4 × 8 = 6^2 4 5 × 9 = 7^2 4 1 × 5 = 3^2 4 2 × 6 = 4^2 4 3 × 7 = 5^2 4 We can see that on the left side both the numbers ar ...

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Byju's Answer

Standard VIII

Mathematics

Visualizing Distributive Property

Look at the p...

Question

Look at the pattern

$1 \times 5 = 3^{2} - 4 2 \times 6 = 4^{2} - 4 3 \times 7 = 5^{2} - 4$

The next lines of the given pattern is equal to

$4 \times 8 = 6^{2} - 4 5 \times 9 = 7^{2} - 4$

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$4 \times 8 = 5^{2} - 5$

$5 \times 9 = 6^{2} - 5$

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$4 \times 9 = 6^{2} - 4$

$5 \times 8 = 7^{2} - 4$

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$4 \times 8 = 6^{2} - 5$

$5 \times 9 = 7^{2} - 6$

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Solution

The correct option is A
$4 \times 8 = 6^{2} - 4 5 \times 9 = 7^{2} - 4$

$1 \times 5 = 3^{2} - 4 2 \times 6 = 4^{2} - 4 3 \times 7 = 5^{2} - 4$

We can see that on the left side both the numbers are increasing by 1 and on the right side the first term is increasing by 1 and the second term is a constant (4)

So, the next line will be equal to

$(3 + 1) \times (7 + 1) = (5 + 1)^{2} - 4$

$(3 + 2) \times (7 + 2) = (5 + 2)^{2} - 4$

$\Rightarrow 4 \times 8 = 6^{2} - 4$

$5 \times 9 = 7^{2} - 4$

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Similar questions

Q. Why this series occurs in square numbers.

0 \times 0 = 0, 1 \times 1 = 1 d i f f e r e n c e = 1 1 \times 1 = 1, 2 \times 2 = 4 d i f f e r e n c e = 3 2 \times 2 = 4, 3 \times 3 = 9 d i f f e r e n c e = 5 3 \times 3 = 9, 4 \times 4 = 16 d i f f e r e n c e = 7 4 \times 4 = 16, 5 \times 5 = 25 d i f f e r e n c e = 9 5 \times 5 = 25, 6 \times 6 = 36 d i f f e r e n c e = 11 6 \times 6 = 36, 7 \times 7 = 49 d i f f e r e n c e = 13 7 \times 7 = 49, 8 \times 8 = 64 d i f f e r e n c e = 15

Q. Look carefully for the pattern, and then choose which pair of numbers comes next:

2 3 4 5 6 4 8

Q. Look at the following pattern:
a)

28 = 2^{2} \times 7^{1}

, Total number of factors

(2 + 1) (1 + 1) = 3 \times 2 = 6

28

is divisible by

6

factors i.e.

1, 2, 4, 7, 14, 28

. Find the pattern.

Q. Observe the following pattern

(1 \times 2) + (2 \times 3) = \frac{2 \times 3 \times 4}{3}

(1 \times 2) + (2 \times 3) + (3 \times 4) = \frac{3 \times 4 \times 5}{3}

(1 \times 2) + (2 \times 3) + (3 \times 4) + (4 \times 5) = \frac{4 \times 5 \times 6}{3}

and find the value of
(1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + (5 × 6)

Question 5

Study the pattern:
$\begin{matrix} 1 \times 8 + 1 = 9; & 12 \times 8 + 2 = 98; & 123 \times 8 + 3 = 987 1234 \times 8 + 4 = 9876; & 12345 \times 8 + 5 = 98765 \end{matrix}$

Write the next two steps. Can you say how the pattern works?

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Look at the pattern 1×5=32−42×6=42−43×7=52−4 The next lines of the given pattern is equal to

Look at the pattern

$1 \times 5 = 3^{2} - 4 2 \times 6 = 4^{2} - 4 3 \times 7 = 5^{2} - 4$

The next lines of the given pattern is equal to