Sarthaks Test
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Find the product.

(i) (a + b) (c − d) + (a − b) (c + d) + 2 (ac + bd)

(ii) (x + y) (2x + y) + (x + 2y) (x − y)

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(i) (a + b) (c − d) + (a − b) (c + d) + 2 (ac + bd)

= a (c − d) + b (c − d) + a (c + d) − b (c + d) + 2 (ac + bd)

= ac − ad + bc − bd + ac + ad − bc − bd + 2ac + 2bd

= (ac + ac + 2ac) + (ad − ad) + (bc − bc) + (2bd − bd − bd)

= 4ac

(ii) (x + y) (2x + y) + (x + 2y) (x − y)

= x (2x + y) + y (2x + y) + x (x − y) + 2y (x − y)

= 2x2 + xy + 2xy + y2 + x2 − xy + 2xy − 2y2

= (2x2 + x2) + (y2 − 2y2) + (xy + 2xy − xy + 2xy)

= 3x2 − y2 + 4xy

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