From the sum of  3×3+7×2-5x+1 and 5×3-9×2+7x-25 subtract -6×3+2×2-6x-8 we get ____.

# From the sum of  and ${5x}^{3}-{9x}^{2}+7x-25$ subtract ${-6x}^{3}+{2x}^{2}-6x-8$ we get ____.

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### Solution:

The sum of ${3x}^{3}+{7x}^{2}-5x+1$ and ${5x}^{3}-{9x}^{2}+7x-25$ is
${3x}^{3}+{7x}^{2}-5x+1+{5x}^{3}-{9x}^{2}+7x-25$
=${7x}^{3}-{2x}^{2}+2x-24$
Now the required polynomial is ${7x}^{3}-{2x}^{2}+2x-24-\left({-6x}^{3}+{2x}^{2}-6x-8\right)$
=${7x}^{3}-{2x}^{2}+2x-24{+6x}^{3}-{2x}^{2}+6x+8$
=${13x}^{3}-{4x}^{2}+8x-16$
From the sum of  and ${5x}^{3}-{9x}^{2}+7x-25$ subtract ${-6x}^{3}+{2x}^{2}-6x-8$ we get ${13x}^{3}-{4x}^{2}+8x-16$

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