Which of the following equation-s is-are correct-i- nbsp- -a - b - c-2 - a-2 - b-2 - c-2 - 2-ab - bc - ca-ii- nbsp- -a - b-3 - a-3 - b-3 - 3ab-a - b-iii- nbsp-a - b-3 - a-3 - b-3 - 3ab-a - b-iv- nbsp-a-2 - b-2 - -a - b-a - b-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Binomial Coefficients

Which of the ...

Question

Which of the following equation/s is/are correct?

$i) (a + b + c)^2 = a^2 + b^2 + c^2 - 2(ab + bc + ca)$
$ii) (a + b)^3 = a^3 + b^3 + 3ab(a - b)$
$iii) (a − b)^3 = a^3 - b^3 - 3ab(a + b)$
$iv) a^2 - b^2 = (a + b)(a - b)$

Open in App

Solution

We have the following identities:
$(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$
$(a + b)^3 = a^3 + b^3 + 3ab(a + b)$
$(a - b)^3 = a^3 - b^3 - 3ab(a - b)$
$a^2 - b^2 = (a + b)(a − b)$

Suggest Corrections

Similar questions

Find $\frac{(a^{2} - b^{2})^{3} + (b^{2} - c^{2})^{3} + (c^{2} - a^{2})^{3}}{(a - b)^{3} + (b - c)^{3} + (c - a)^{3}} =$

Which of the following equation/s is/are correct?

$i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} - 2 (a b + b c + c a)$
$i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)$
$i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)$
$i v) a^{2} - b^{2} = (a + b) (a - b)$

Q. Which of the following equations are correct?

(i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)

(i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)

(i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)

(i v) a^{2} - b^{2} = (a + b) (a - b)

a^{3}

–

b^{3}

(a - b)^{3}

+ 3ab(a - b)

Q. If

(a_{1}, a_{2}, a_{3})

(b_{1}, b_{2}, b_{3})

and

(c_{1}, c_{2}, c_{3})

are linearly independent and

x (a_{1}, a_{2}, a_{3}) + y (b_{1}, b_{2}, b_{3}) + z (c_{1}, c_{2}, c_{3}) = 0

then

Join BYJU'S Learning Program

Which of the following equation/s is/are correct?

\(i) (a + b + c)^2 = a^2 + b^2 + c^2 - 2(ab + bc + ca)\)
\(ii) (a + b)^3 = a^3 + b^3 + 3ab(a - b)\)
\(iii) (a − b)^3 = a^3 - b^3 - 3ab(a + b)\)
\(iv) a^2 - b^2 = (a + b)(a - b)\)

We have the following identities:
\((a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)\)
\((a + b)^3 = a^3 + b^3 + 3ab(a + b)\)
\((a - b)^3 = a^3 - b^3 - 3ab(a - b)\)
\(a^2 - b^2 = (a + b)(a − b)\)

Which of the following equation/s is/are correct? \(i) (a + b + c)^2 = a^2 + b^2 + c^2 - 2(ab + bc + ca)\) \(ii) (a + b)^3 = a^3 + b^3 + 3ab(a - b)\) \(iii) (a − b)^3 = a^3 - b^3 - 3ab(a + b)\) \(iv) a^2 - b^2 = (a + b)(a - b)\)

We have the following identities: \((a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)\) \((a + b)^3 = a^3 + b^3 + 3ab(a + b)\) \((a - b)^3 = a^3 - b^3 - 3ab(a - b)\) \(a^2 - b^2 = (a + b)(a − b)\)

Which of the following equation/s is/are correct?

\(i) (a + b + c)^2 = a^2 + b^2 + c^2 - 2(ab + bc + ca)\)
\(ii) (a + b)^3 = a^3 + b^3 + 3ab(a - b)\)
\(iii) (a − b)^3 = a^3 - b^3 - 3ab(a + b)\)
\(iv) a^2 - b^2 = (a + b)(a - b)\)

We have the following identities:
\((a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)\)
\((a + b)^3 = a^3 + b^3 + 3ab(a + b)\)
\((a - b)^3 = a^3 - b^3 - 3ab(a - b)\)
\(a^2 - b^2 = (a + b)(a − b)\)