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Simplify the following expression:
[tex]\[ -12xy + 3x^2 - x(3 - 5y) + 3xy \][/tex]

Sagot :

GinnyAnswer
Certainly! Let's simplify the given algebraic expression step by step.

Given expression:
[tex]\[ -12xy + 3x^2 - x(3 - 5y) + 3xy \][/tex]

Step 1: Distribute and combine like terms

First, distribute [tex]\( x \)[/tex] through the expression inside the parentheses:

[tex]\[ -12xy + 3x^2 - x \cdot 3 + x \cdot 5y + 3xy \][/tex]
[tex]\[ -12xy + 3x^2 - 3x + 5xy + 3xy \][/tex]

Next, combine the like terms involving [tex]\( xy \)[/tex]:

[tex]\[ -12xy + 5xy + 3xy = -12xy + 8xy = -4xy \][/tex]

So, the expression now is:

[tex]\[ 3x^2 - 3x - 4xy \][/tex]

Step 2: Factor the expression if possible

We can factor out a common factor [tex]\( x \)[/tex] from each term:

[tex]\[ x(3x - 3 - 4y) \][/tex]

So, the simplified form of the given expression is:

[tex]\[ x(3x - 3 - 4y) \][/tex]

Thus, the final simplified expression is:

[tex]\[ x(3x - 4y - 3) \][/tex]

So, the original expression [tex]\( -12xy + 3x^2 - x(3 - 5y) + 3xy \)[/tex] simplifies to:

[tex]\[ x(3x - 4y - 3) \][/tex]
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