Mathematics

Mathematics

Problem

Simplify −12m3(6m2−3m+4)-\dfrac{1}{2}m^{3}(6m^{2} - 3m + 4) and write the result in descending powers of mm.
Intuitive explanation

This is about distributing a monomial across a polynomial — a foundational algebraic skill. The key is to multiply −12m3-\frac{1}{2}m^3 by each term inside the parentheses separately, using the exponent rule ma⋅mb=ma+bm^a \cdot m^b = m^{a+b}. Then arrange your three resulting terms from highest to lowest power of mm.

Intuitive explanation

This is about distributing a monomial across a polynomial — a foundational algebraic skill. The key is to multiply −12m3-\frac{1}{2}m^3 by each term inside the parentheses separately, using the exponent rule ma⋅mb=ma+bm^a \cdot m^b = m^{a+b}. Then arrange your three resulting terms from highest to lowest power of mm.

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