To find the product of the expression \( x^2(4x^2 - 5 - 3x) \) using the distributive property, we need to distribute \( x^2 \) to each term in the parentheses.
Let's break it down:
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Distribute \( x^2 \) to \( 4x^2 \): \[ x^2 \cdot 4x^2 = 4x^{2+2} = 4x^4 \]
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Distribute \( x^2 \) to \( -5 \): \[ x^2 \cdot (-5) = -5x^2 \]
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Distribute \( x^2 \) to \( -3x \): \[ x^2 \cdot (-3x) = -3x^{2+1} = -3x^3 \]
Now, putting all these results together: \[ 4x^4 - 3x^3 - 5x^2 \]
Next, we'll write this in standard form, which means we arrange the polynomial in descending order of the exponents: \[ 4x^4 - 3x^3 - 5x^2 \]
So, the final answer in standard form is: \[ 4x^4 - 3x^3 - 5x^2 \]