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Question

Answer

$((y - 5)^{2} - 2)^{2} - y + 3 = y^{4} - 20 y^{3} + 146 y^{2} - 461 y + 532$

Explanation

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$((y - 5)^{2} - 2)^{2} - y + 3 \overset{◯}{1} (1 y^{2} - 10 y + 25 - 2)^{2} - y + 3 \overset{◯}{2} (1 y^{2} - 10 y + 23)^{2} - y + 3 \overset{◯}{3} \overset{◯}{4} y^{4} - 20 y^{3} + 146 y^{2} - 460 y + 529 - y + 3 \overset{◯}{5} y^{4} - 20 y^{3} + 146 y^{2} - 461 y + 532$
①	Find $(y - 5)^{2}$ using formula. $(A - B)^{2} = A^{2} - 2 \cdot A \cdot B + B^{2}$ where $A = y$ and $B = 5$ . $(y - 5)^{2} = y^{2} - 2 \cdot y \cdot 5 + 5^{2} = y^{2} - 10 y + 25$
②	Combine like terms: $y^{2} - 10 y + 25 - 2 = y^{2} - 10 y + 23$
③	Multiply each term of $(y^{2} - 10 y + 23)$ by each term in $(y^{2} - 10 y + 23)$ . $(y^{2} - 10 y + 23) \cdot (y^{2} - 10 y + 23) = y^{4} - 10 y^{3} + 23 y^{2} - 10 y^{3} + 100 y^{2} - 230 y + 23 y^{2} - 230 y + 529$
④	Combine like terms: $y^{4} - 10 y^{3} + 23 y^{2} - 10 y^{3} + 100 y^{2} - 230 y + 23 y^{2} - 230 y + 529 = = y^{4} - 20 y^{3} + 146 y^{2} - 460 y + 529$
⑤	Combine like terms: $y^{4} - 20 y^{3} + 146 y^{2} - 460 y + 529 - y + 3 = y^{4} - 20 y^{3} + 146 y^{2} - 461 y + 532$

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