Question 58

The simpliﬁed form of $$(4x + 3)^2(3x - 5) - (4x^{3} - 12x^2 + 9x - 20)$$ is

Solution

Expression : $$(4x + 3)^2(3x - 5) - (4x^{3} - 12x^2 + 9x - 20)$$

= $$[(16x^2 + 24x + 9) (3x - 5)] - (4x^3 - 12x^2 + 9x - 20)$$

= $$[(48x^3 - 80x^2) + (72x^2 - 120x) + (27x - 45)] + (-4x^3 + 12x^2 - 9x + 20)$$

= $$(48x^3 - 4x^3) + (-80x^2 + 72x^2 + 12x^2) + (-120x + 27x - 9x) + (-45 + 20)$$

= $$44x^3 + 4x^2 - 102x - 25$$

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