Question

Find the factors of the following quadratic expressions.


`7(a + b) {}^(2) + 8(a + b) + 1`

Answer 1

Let x = a + b

7(a + b)² + 8(a + b) + 1 = 7x² + 8x + 1
7(a + b)² + 8(a + b) + 1 = (7x + 1)(x + 1)

Substitute x = a + b back

7(a + b)² + 8(a + b) + 1 = (7(a+b) + 1)((a+b) + 1)
7(a + b)² + 8(a + b) + 1 = (7a + 7b + 1)(a + b + 1)


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Answer: (7a + 7b + 1)(a + b + 1)
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