Math Problem Statement

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

Solution

To solve the equation (a+b+2c+3d)(a−b−2c+3d)=(a−b+2c−3d)(a+b−2c−3d)(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)(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^

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
FOIL Method

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12

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