What is (ax+by)(cx+dy)?

Apr 9, 2018

If you are asking for the expansion, it is as follows.

Explanation:

$\left(a x + b y\right) \left(c x + \mathrm{dy}\right) = a x \times c x + a x \times \mathrm{dy} + b y \times c x + b y \times \mathrm{dy}$

$= a c {x}^{2} + a \mathrm{dx} y + b c x y + b {\mathrm{dy}}^{2}$

$= a c {x}^{2} + \left(a d + b c\right) x y + b {\mathrm{dy}}^{2}$

Apr 9, 2018

$\left(a x + b y\right) \left(c x + \mathrm{dy}\right) = a c {x}^{2} + a \mathrm{dx} y + b c x y + b {\mathrm{dy}}^{2}$

Explanation:

Multiplying binomials with the same exponent on multiple coefficients(EX: $a x$; $c x$) will result in the variable $\left(x\right)$ being given a power of $2$ and the coefficients (a; c) combining through multiplication. EX:

$a x \times c x = a c {x}^{2}$

When variables are different they are also put together at the end of the term. EX:

$a x \times \mathrm{dy} = a \mathrm{dx} y$