Question

39. a²c² -b²c² -4a²d² +4b²d²

Answer 1

The simplified expression for the given algebraic expression $a^{2} c^{2} -b^{2} c^{2} -4a^{2} d^{2} +4b^{2} d^{2}$ is $(a+b)(a-b)(c+2d)(c-2d)$

As per the question statement, we are given an algebraic expression

$a^{2} c^{2} -b^{2} c^{2} -4a^{2} d^{2} +4b^{2} d^{2}$ and we are supposed to solve and simplify it.

Solution:

$a^{2} c^{2} -b^{2} c^{2} -4a^{2} d^{2} +4b^{2} d^{2}\\c^{2} (a^{2} -b^{2})-4d^{2}(a^{2} -b^{2})\\(a^{2} -b^{2})(c^{2}-4d^{2})\\(a^{2} -b^{2})(c^{2}-(2d)^{2})$

Have used Distributive property for solving and simplifying the above algebraic expression.

Now using the property, $a^{2} -b^{2} =(a+b)(a-b)$

We get,

$(a+b)(a-b)(c+2d)(c-2d)$

Therefore $(a+b)(a-b)(c+2d)(c-2d)$ is our required answer.

• Distributive Property: The same outcome will be obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend separately by the number and then adding the resulting products.

Click the following link to learn more about distributive property:

https://brainly.com/question/5637942

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