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Subtract [tex]\(3x(x - 2y)\)[/tex] from [tex]\(6(x^2 - xy)\)[/tex] and express your answer as a monomial.

Sagot :

GinnyAnswer
Sure, let's solve the problem step by step.

We are given two expressions, and we need to subtract the second expression from the first one:

1. [tex]\(6(x^2 - xy)\)[/tex]
2. [tex]\(3x(x - 2y)\)[/tex]

Step 1: Expand and simplify each expression.

[tex]\[6(x^2 - xy) = 6x^2 - 6xy\][/tex]

[tex]\[3x(x - 2y) = 3x \cdot x - 3x \cdot 2y = 3x^2 - 6xy\][/tex]

Step 2: Subtract the second expression from the first.

[tex]\[(6x^2 - 6xy) - (3x^2 - 6xy)\][/tex]

Step 3: Distribute the negative sign through the terms of the second expression.

[tex]\[6x^2 - 6xy - 3x^2 + 6xy\][/tex]

Step 4: Combine like terms.

[tex]\[6x^2 - 3x^2 - 6xy + 6xy\][/tex]

The [tex]\( -6xy \)[/tex] and [tex]\( +6xy \)[/tex] terms cancel each other out, leaving:

[tex]\[6x^2 - 3x^2 = 3x^2\][/tex]

So, the result expressed as a monomial is:

[tex]\[3x^2\][/tex]

Hence, subtracting [tex]\(3x(x - 2y)\)[/tex] from [tex]\(6(x^2 - xy)\)[/tex] and expressing the answer as a monomial gives us [tex]\(3x^2\)[/tex].
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