Question

Using the identity (a + b)² = a² + 2ab + b², simplify the following:(i) (a + 6)², (ii) (3x + 2y)²; (iii) (2p + 3q)²; (iv) (x² + 5)².

Answer 1

$\large \tt AHOY!! \:$

(i) (a + 6)² [a = a, b = 6]

= (a)² + 2(a)(6) + (6)²

= a² + 12a + 36

(ii) (3x + 2y)² [a = 3x, b = 2y]

= (3x)² + 2(3x)(2y) + (2y)²

= 9x² + 12xy + 4y²

(iii) (2p + 3q)² [a = 2p, b = 3q]

= (2p)² + 2(2p)(3q) + (3q)²

= 4p² + 12pq + 9q²

(iv) (x² + 5)² [a = x², b = 5]

= (x²)² + 2(x²)(5) + (5)²

= x⁴ + 10x² + 25

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