Question 56

The coefficient of $$x^2$$ in $$(2x + y)^3$$ is:

Solution

$$(2x + y)^3$$

= $$(2x)^3 + y^3 + 3.2x.y(2x + y)$$

($$\because (a + b)^3 = a^3 + b^3 + 3ab(a + b)$$)

= $$8x^3 + y^3 + 6xy(2x + y)$$

= $$8x^3 + y^3 + 12x^2y + 6xy^2$$

The coefficient of $$x^2$$ = 12y

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