Question 11 of 43beginner🔧 ApplyShort Answer2 marks

Expand the following using the identity (a + b + c)^2 = a2a^{2} + b2b^{2} + c2c^{2} + 2ab + 2bc + 2ca:

(i)

(p + 3q + 7r)^2

Answer

p2p^{2} + 9q29q^{2} + 49r249r^{2} + 6pq + 42qr + 14rp

(ii)

(3x - 2y + 4z)^2

Answer

9x29x^{2} + 4y24y^{2} + 16z216z^{2} - 12xy - 16yz + 24zx

Explanation

We use the identity (a + b + c)^2 = a2a^{2} + b2b^{2} + c2c^{2} + 2ab + 2bc + 2ca to expand the given expressions. For part (i), we substitute a = p, b = 3q, and c = 7r. For part (ii), we substitute a = 3x, b = -2y, and c = 4z, carefully applying the negative sign during multiplication.

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