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If A=-1+3x^2 and B=x^2+2x-6, find an expression that equals 2A-2B in standard form

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6 votes

Answer:

2A - 2B = 4x^2 - 4x + 10

Explanation:

To find the expression for 2A - 2B, we need to first compute 2A and 2B and then subtract them. Let's start by finding each part separately:

2A:

2A = 2(-1 + 3x^2) = -2 + 6x^2

2B:

2B = 2(x^2 + 2x - 6) = 2x^2 + 4x - 12

Now, subtract 2B from 2A:

2A - 2B = (-2 + 6x^2) - (2x^2 + 4x - 12)

Now, let's combine like terms:

2A - 2B = -2 + 6x^2 - 2x^2 - 4x + 12

Simplify further:

2A - 2B = (6x^2 - 2x^2) + (-2 - 4x + 12)

Combine the x^2 terms and constants:

2A - 2B = 4x^2 - 4x + 10

The expression in standard form that equals 2A - 2B is:

2A - 2B = 4x^2 - 4x + 10

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