Math Problem Statement

Simplify and arrange the following algebraic expressions: (1) 4a^2 - 3b^2 + 2ab + (4a^2 - 4b^2)

Solution

It looks like the image contains a set of algebraic expressions that need to be simplified. Let me break down the steps for you. I'll go ahead and start with the first expression from the list.

Problem (1):
4a23b2+2ab+(4a24b2)4a^2 - 3b^2 + 2ab + (4a^2 - 4b^2)

To simplify this, first remove the parentheses and combine like terms:

4a23b2+2ab+4a24b24a^2 - 3b^2 + 2ab + 4a^2 - 4b^2

Now, combine the terms with a2a^2 and the terms with b2b^2:

(4a2+4a2)+(3b24b2)+2ab(4a^2 + 4a^2) + (-3b^2 - 4b^2) + 2ab

This simplifies to:

8a27b2+2ab8a^2 - 7b^2 + 2ab

So, the simplified expression is: 8a27b2+2ab8a^2 - 7b^2 + 2ab

Would you like me to go over the rest of the expressions? Let me know if you need further details or explanations!

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of expressions
Combining like terms

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10