Question

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Explanation:

Step1: Simplify the right - hand side expression

First, we need to remove the parentheses. When we subtract a polynomial \((-3x^{2}+3x - 7)\), we can rewrite the subtraction as adding the opposite. So \((10x - 15)-(-3x^{2}+3x - 7)=10x - 15 + 3x^{2}-3x + 7\).

Step2: Combine like terms

For the \(x\) - terms: \(10x-3x = 7x\). For the constant terms: \(-15 + 7=-8\). And the \(x^{2}\) term remains \(3x^{2}\). So combining like terms, we get \(3x^{2}+7x - 8\).

In the parts - whole model, the whole (the left - hand side) is equal to the result of subtracting the second part \((-3x^{2}+3x - 7)\) from the first part \((10x - 15)\). After simplification, the whole is \(3x^{2}+7x - 8\), the first part is \(10x - 15\) and the second part is \(-3x^{2}+3x - 7\).

Answer:

The left - hand side (the whole) is \(3x^{2}+7x - 8\), the first part (the upper - left in the lower box) is \(10x - 15\) and the second part (the upper - right in the lower box) is \(-3x^{2}+3x - 7\) (or we can say the whole is \(3x^{2}+7x - 8\), and the two parts are \(10x - 15\) and \(-(-3x^{2}+3x - 7)\) which simplifies to \(3x^{2}-3x + 7\), but the more direct way is to simplify the right - hand side to get the whole as \(3x^{2}+7x - 8\) with parts \(10x - 15\) and \(-3x^{2}+3x - 7\)).

If we just fill the blank on the left - hand side: \(\boldsymbol{3x^{2}+7x - 8}\)