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25 votes
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Simplify (x − 4)(4x2 + x − 6).

User Jeje Doudou
by
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1 Answer

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20 votes

Answer: To simplify the expression (x - 4)(4x^2 + x - 6), you can use the distributive property, which states that you can multiply a number or expression by each term inside a set of parentheses.

Here is the process for simplifying the expression:

Multiply the first term, "x - 4", by the first term inside the second set of parentheses, "4x^2": (x - 4)(4x^2) = 4x^3 - 16x^2

Multiply the first term, "x - 4", by the second term inside the second set of parentheses, "x": (x - 4)(x) = x^2 - 4x

Multiply the first term, "x - 4", by the third term inside the second set of parentheses, "-6": (x - 4)(-6) = -6x + 24

Add the three products together: 4x^3 - 16x^2 + x^2 - 4x - 6x + 24 = 4x^3 - 16x^2 + x^2 - 10x + 24 = 4x^3 - 15x^2 - 10x + 24

The simplified expression is: 4x^3 - 15x^2 - 10x + 24

So, (x - 4)(4x^2 + x - 6) = 4x^3 - 15x^2 - 10x + 24.

User Tada
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