Question

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If a, b, c and d are four consecutive multiples of 10 and a < b < v < d, what is the value of (a-c)(b-d)?

(ಠ_ಠ) Answer this correctly with good explanation !!
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Answer 1

Answer:

$\huge\mathcal{\green{Annyeonghaseyo!}}$

$\huge\mathfrak{\red{Answer}}$

$\huge\fbox{\purple{ :➝ \ 400}}$

Step-by-step explanation:

☆ Question:-

If a, b, c and d are four consecutive multiples of 10 and a < b < c < d, what is the value of (a-c)(b-d)?

☆ Given:-

• a, b, c and d are four consecutive multiples of 10.

• a < b < c < d

☆ To find:-

• (a-c)(d-b)

☆ Required Solution:-

As given that a, b, c and d are consecutive numbers and are multiples of 10.

$\huge\mathcal{\green{Therefore,}}$

a, b, c and d are in Arithmetic progression with common difference of 10.

it means that

First term is a

second term, b is a+10

Third term, c is a+20

$\huge\mathcal{\green{And}}$

Fourth term, d is a+ 30

$\huge\mathcal{\green{Now,}}$

a<c and b<d, therefore, (a-c) will be negative as it will be <0 & (d-b) will be positive as it will be >0

: ➝ (a-c)(d-b)= [{a-(a+20)}{(a+30)-(a+10)}]

= [{a-a+20}{a+30-a-10}]

= [(20)(20)]

= 400

$\huge\mathcal{\green{All \ the \ very \ best!}}$

$\huge\mathfrak{\red{@MissTranquil}}$

$\huge\fbox{\orange{be \ brainly}}$

Answer 2

$\large{\underbrace{\underline{\bf{Correct\;Question:-}}}}$

Q) If a, b, c and d are four consecutive multiples of 10 and a < b < c < d, what is the value of (a-c) (b-d) ?

$\large{\underbrace{\underline{\bf{Required\;Answer:-}}}}$

» It is given that a, b, c and d are the consecutive multiples of 10 .

• When a number is multiplied by consecutive numbers , it forms Consecutive multiples.
• The adjacent multiples differ with a common difference which is the number itself.
• Eg : Consecutive multiples of 3 → 3,6,9,12.., in this, adjacent terms differ by 3.

so, if

• a = a

then,

• b = a + 10
• c = a + 10 + 10 = a + 20
• d = a + 10 + 10 + 10 = a + 30

Now,

$\colon \rarr \sf \: (a - c)(b - d)$

Here,put :

• a = a
• b = a+10
• c = a+20
• d = a+30

$\colon \rarr \sf \: \{a - (a + 20) \} \{(a + 10) - (a + 30) \} \\ \\ \colon \rarr \sf \: ( \cancel{a} - \cancel{a }- 20)( \cancel{a} + 10 - \cancel{ a} - 30) \\ \\ \colon \rarr \sf \: ( - 20)(10 - 30) \\ \\ \colon \rarr \sf \: - 20 \times - 20 \\ \\ \dashrightarrow \underline{\boxed{ \pink{ \bf(a - c)(b - d) = \sf{\red{400}}}}}$

So,

» The value of (a-c) (b-d) = 400 .

$\tt{\purple{Purple~Ya'}}$

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