Question 16

The expression $$49(a + b)^2 - 46(a - b)^2$$ is factorized into $$(la + mb)(na + pb)$$, then the numerical value of $$(l + m + n + p)$$ is

Correct Answer: 28

Solution

An expression of the form $$u^2(a+b)^2 - v^2(a-b)^2$$ is a difference of two squares, so it factorises as $$[(u - v)a + (u + v)b][(u + v)a + (u - v)b]$$. The four coefficients then add up to $$(u - v) + (u + v) + (u + v) + (u - v) = 4u$$. Here $$u = 7$$, so $$l + m + n + p = 4 \times 7 = 28$$.

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