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Answer :
The correct simplification of the expression [tex]\(-4x^2(6x - 5x^2 - 5)\)[/tex] is [tex]\(-24x^3 + 20x^4 + 20x^2\).[/tex]
To simplify the given expression, we need to distribute the [tex]\(-4x^2\)[/tex] term across each term inside the parentheses:
[tex]\[ -4x^2(6x) = -24x^3 \] \[ -4x^2(-5x^2) = 20x^4 \] \[ -4x^2(-5) = 20x^2 \][/tex]
Now, we combine these results to get the simplified expression:
[tex]\[ -24x^3 + 20x^4 + 20x^2 \][/tex]
The terms [tex]\(20x^4\)[/tex], [tex]\(24x^3\)[/tex], and [tex]\(20x^2\)[/tex] appear in both the given expression and the simplified expression, but with different signs. This is because the distributive property requires us to multiply the [tex]\(-4x^2\)[/tex] by each term inside the parentheses, which includes negating each product since the initial coefficient is negative.
The given expression also includes a series of terms with subtraction and addition, which seem to be an attempt to simplify the expression. However, the correct simplification does not involve adding and then subtracting the same terms. Instead, it is the direct result of the distribution of [tex]\(-4x^2\)[/tex] across the terms within the parentheses.
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Rewritten by : Barada
If you would like to solve -4x^2 * (6x - 5x^2 - 5), you can do this using the following steps:
-4x^2 * (6x - 5x^2 - 5) = -4x^2 * 6x + 4x^2 * 5x^2 + 4x^2 * 5 = -24x^3 + 20x^4 + 20x^2 = 20x^4 - 24x^3 + 20x^2
The correct result would be 20x^4 - 24x^3 + 20x^2.
-4x^2 * (6x - 5x^2 - 5) = -4x^2 * 6x + 4x^2 * 5x^2 + 4x^2 * 5 = -24x^3 + 20x^4 + 20x^2 = 20x^4 - 24x^3 + 20x^2
The correct result would be 20x^4 - 24x^3 + 20x^2.
