Evaluate the following product without multiplying directly:
$78 \times 84$

If $x^{2}-10x+21=(x+m)(x+n)$,then $m+n = \ldots$

Give a possible expression for the length of a side of a square whose area is $(9x^2 + 30x + 25)$ square units, where $(x > 0)$.

By the Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = x^{3} - 6x^{2} + 2x - 4$ and $g(x) = 1 - \frac{3}{2}x$.

Factorise $8x^{3} + 125y^{3} + 343 - 210xy$.

Expand: $(x+3y-5z)^{2}$