Simplify 14p^2+27pq-20q^2

Problem

14*p2+27*p*q−20*q2

Solution

1. Identify the coefficients of the quadratic expression in the form a*p2+b*p*q+c*q2 where a=14 b=27 and c=−20

2. Calculate the product of a and c which is 14×−20=−280

3. Find two numbers that multiply to −280 and add to the middle coefficient b=27 These numbers are 35 and −8

4. Rewrite the middle term 27*p*q using the two numbers found: 35*p*q−8*p*q

14*p2+35*p*q−8*p*q−20*q2

5. Factor by grouping the first two terms and the last two terms.

7*p*(2*p+5*q)−4*q*(2*p+5*q)

6. Factor out the common binomial (2*p+5*q)

(7*p−4*q)*(2*p+5*q)

Final Answer

14*p2+27*p*q−20*q2=(7*p−4*q)*(2*p+5*q)

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