(a+b+2c+3d)(a-b-2c+3d)=(a-b+2c-3d)(a+b-2c-3d)

To solve the equation \((a+b+2c+3d)(a-b-2c+3d)=(a-b+2c-3d)(a+b-2c-3d)\), let's first expand both sides of the equation.

### Left Side: \((a+b+2c+3d)(a-b-2c+3d)\)
Using the distributive property (FOIL method), we get:

\[
\begin{aligned}
(a+b+2c+3d)(a-b-2c+3d) &= a(a-b-2c+3d) + b(a-b-2c+3d) + 2c(a-b-2c+3d) + 3d(a-b-2c+3d) \\
&= a^2 - ab - 2ac + 3ad + ab - b^2 - 2bc + 3bd + 2ac - 2bc - 4c^2 + 6cd + 3ad - 3bd - 6cd + 9d^2 \\
&= a^2 - b^

Explore how to solve the quadratic equation (a+b+2c+3d)(a-b-2c+3d) = (a-b+2c-3d)(a+b-2c-3d) step-by-step. Learn about the distributive property and FOIL method application in algebraic equations. Suitable for high school students studying algebra.

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