Find the value of the polynomial $a^{3} + 3 a^{2} b + 2 a b - b^{2}$ at $a = - 2$ and $b = 3$ . [2 MARKS]

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The value of the polynomial $a^{3} + 3 a^{2} b + 2 a b - b^{2}$ at a = -2 and b = 3

$a^{3} + 3 a^{2} b + 2 a b - b^{2}$
On substituting the values of a and b in the above expression we get:

$= (- 2)^{3} + 3 \times (- 2)^{2} \times 3 + 2 \times (- 2) \times 3 - 3^{2}$

$= - 8 + 36 - 12 - 9 = 7$

So, the value of the polynomial $a^{3} + 3 a^{2} b + 2 a b - b^{2}$ at $a = - 2$ and $b = 3$ is 7.

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