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Expand $(az^2+bz+c)(dz^2+pz+q)$.

Simplify $(ax+b)(cx+d)-(ax+d)(cx+b)$. Answer is a multiple of $x$.

Simplify $(ax+by)(cx+dy)-(ax+dy)(cx+by)$. Answer is a multiple of $xy$.

Expand $(ax+b)(cx+d)$.

Expand $(ay+b)(cy+d)(py+q)$.

Includes a video expanding three brackets, however uses the variable $x$ rather than $y$.

Expand $(az^2+bz+c)(pz+q)$.

Expand $(pw+q)(aw^2+bw+c)$.

Find eigenvalues and eigenvectors of $A$ $2 \times 2$ matrix.

Determine if various combinations of vectors are defined or not.

When are vectors $\boldsymbol{A,\;B}$ perpendicular?