Factorize the equation $a^{2} + b^{2} - c^{2} - d^{2} + 2 a b - 2 c d$

(a + b + c + d) (a + b + c - d)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(a + b - c + d) (a c - d)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(a - b + c + d) (b + c - d)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(a + b + c - d) (a + b + c - d)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $(a + b + c + d) (a + b + c - d)$
$a^{2} + b^{2} - c^{2} - d^{2} + 2 a b - 2 c d$
$= (a^{2} + 2 a b + b^{2}) - (c^{2} + 2 c d + d^{2})$
Using,
$(a + b)^{2} = a^{2} + 2 a b + b^{2}$
$= (a + b)^{2} - (c + d)^{2}$
Using,
$(a^{2} - b^{2}) = (a + b) (a - b)$
$= (a + b + c + d) (a + b - c - d)$

Suggest Corrections

Similar questions

2 (a b + c d) - a^{2} - b^{2} + c^{2} + d^{2}

(a^{2} + b^{2}) x^{2} - 2 (a c + b d) x + c^{2} + d^{2} = 0

a d = \sqrt{b c}

a b = \sqrt{c d}

a, b, c, d

(b - c)^{2} + (c - a)^{2} + (d - b)^{2} = (a - d)^{2}

a, b, c, d

{(a - c)}^{2} + {(c - b)}^{2} + {(b - d)}^{2} - {(d - a)}^{2}

Join BYJU'S Learning Program