Question 3(iv)
Simplify:
(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)

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Solution

(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)
=a(c-d)+b(c-d)+a(c+d)-b(c+d)+2ac+2bd
=ac-ad+bc-bd+ac+ad-bc-bd+2ac+2bd
=ac+ac-ad+ad+bc-bc-bd-bd+2ac+2bd
=4ac

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Question 3(iv)
Simplify:
(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)

(a + b) (c - d) + (a - b) (c + d) + 2 (a c + b d)

Question 5
ABCD is a quadrilateral. Is AB + BC + CD + DA < 2 (AC + BD)?

Δ A B C

2 A B^{2} = 2 A C^{2} + B C^{2}

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

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