Question

Factorise: p^2 +p - (a+1)(a+2)


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Answer 1

Step-by-step explanation:

p² + p - (a+1)(a+2)

= p² + (a + 2)p - (a + 1)p - (a+1)(a+2) [∵ a+2-a+1 = 1]

= p(p+a+2) - (a+1)(p+a+2)

= (p-a-1)(p+a+2)

note that in any mid term factorisation case, our main motive is to divide the midterm into two terms such that the product of their coefficients is equal to the product of the coefficients of the other terms. like in this case, the product of the coefficients of the other terms is -(a+1)(a+2), so i divided the middle term into (a+2) and -(a+1), so that their products are equal