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Advanced Math / Equivalent expressions Difficulty: Medium

$(5 x^{3} - 3) - (- 4 x^{3} + 8)$

The given expression is equivalent to $b x cubed minus 11$ , where $b$ is a constant. What is the value of $b$ ?

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Explanation

The correct answer is $9$ . The given expression can be rewritten as $(5 x^{3} - 3) + (- 1) (- 4 x^{3} + 8)$ . By applying the distributive property, this expression can be rewritten as $5 x^{3} - 3 + 4 x^{3} + (- 8)$ , which is equivalent to $(5 x^{3} + 4 x^{3}) + (- 3 + (- 8))$ . Adding like terms in this expression yields $9 x cubed minus 11$ . Since it's given that $(5 x^{3} - 3) - (- 4 x^{3} + 8)$ is equivalent to $b x cubed minus 11$ , it follows that $9 x cubed minus 11$ is equivalent to $b x cubed minus 11$ . Therefore, the coefficients of $x^{3}$ in these two expressions must be equivalent, and the value of $b$ must be $9$ .