QuestionJuly 15, 2025

Factor using the sum or difference of cubes.(Check by multiplying.) y^3+64 Part 1 of 2 Factor using the sum or difference of cubes. y^3+64=(y+4)(y^2-4y+16) Part: 1/2 Part 2 of 2 Check: (y+4)(y^2-4y+16)=y^3-square y^2+square y+square y^2-16y+64=y^3+64

Factor using the sum or difference of cubes.(Check by multiplying.) y^3+64 Part 1 of 2 Factor using the sum or difference of cubes. y^3+64=(y+4)(y^2-4y+16) Part: 1/2 Part 2 of 2 Check: (y+4)(y^2-4y+16)=y^3-square y^2+square y+square y^2-16y+64=y^3+64
Factor using the sum or difference of cubes.(Check by multiplying.) y^3+64 Part 1 of 2 Factor using the sum or difference of cubes. y^3+64=(y+4)(y^2-4y+16) Part: 1/2 Part 2 of 2 Check: (y+4)(y^2-4y+16)=y^3-square y^2+square y+square y^2-16y+64=y^3+64

Solution
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Answer

The factorization is correct: y^3 + 64 = (y + 4)(y^2 - 4y + 16). Explanation 1. Identify the sum of cubes Recognize y^3 + 64 as a sum of cubes: y^3 + 4^3. 2. Apply the sum of cubes formula Use **(a^3 + b^3) = (a + b)(a^2 - ab + b^2)** with a = y and b = 4. Substitute to get (y + 4)(y^2 - 4y + 16). 3. Verify by multiplying Expand (y + 4)(y^2 - 4y + 16): - First, y \cdot (y^2 - 4y + 16) = y^3 - 4y^2 + 16y. - Second, 4 \cdot (y^2 - 4y + 16) = 4y^2 - 16y + 64. - Combine: y^3 - 4y^2 + 16y + 4y^2 - 16y + 64. 4. Simplify the expression Combine like terms: y^3 + 0y^2 + 0y + 64 = y^3 + 64.

Explanation

1. Identify the sum of cubes<br /> Recognize $y^3 + 64$ as a sum of cubes: $y^3 + 4^3$.<br /><br />2. Apply the sum of cubes formula<br /> Use **$(a^3 + b^3) = (a + b)(a^2 - ab + b^2)$** with $a = y$ and $b = 4$.<br /> Substitute to get $(y + 4)(y^2 - 4y + 16)$.<br /><br />3. Verify by multiplying<br /> Expand $(y + 4)(y^2 - 4y + 16)$:<br />- First, $y \cdot (y^2 - 4y + 16) = y^3 - 4y^2 + 16y$.<br />- Second, $4 \cdot (y^2 - 4y + 16) = 4y^2 - 16y + 64$.<br />- Combine: $y^3 - 4y^2 + 16y + 4y^2 - 16y + 64$.<br /><br />4. Simplify the expression<br /> Combine like terms: $y^3 + 0y^2 + 0y + 64 = y^3 + 64$.
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