## Algebra 1

$-12x^6 + 40x^4$
(i) $a^m \cdot a^n = a^{m+n}$ (ii) $x(y-z) = xy - xz$ Use rule (ii) above by multiplying $-4x^3$ to each term of the binomial to obtain: $=-4x^3(3x^3) - (-4x^3)(10x)$ Multiply the coefficients together, and then apply rule (i) above to obtain: $\\=-12x^{3+3}-(-40x^{3+1}) \\=-12x^6-(-40x^4) \\=-12x^6 + 40x^4$