Factor: 1. $$ m^{3}+27 $$ [A] $$ (m+3)^{3} $$ [B] $$ (m+3)\left(m^{2}+9\right) $$ $$ [C](m+3)\left(m^{2}-3 m+9\right) $$ [D] $$ (m-3)\left(m^{2}+3 m+9\right) $$ 2. $$ 8 b^{3}-125 $$ [A] $$ (2 b-5)\left(4 b^{2}+10 b+25\right) $$ [B] $$ (2 b-5)^{3} $$ $$ [C](2 b-5)\left(4 b^{2}+25\right) $$ [D] $$ (2 b+10)\left(4 b^{2}-5 b+25\right) $$ 3. $$ 27 e^{3}-8 $$ $$ [\mathrm{A}](3 e+6)\left(9 e^{2}-2 e+4\right) $$ [B] $$ (3 e-2)^{3} $$ [C] $$ (3 e-2)\left(9 e^{2}+6 e+4\right) $$ [D] $$ (3 e-2)\left(9 e^{2}+4\right) $$ 4. $$ 8 r^{3}+125 $$ $$ [A](2 r+5)\left(4 r^{2}+25\right) $$ [B] $$ (2 r+5)\left(4 r^{2}-10 r+25\right) $$ [C] $$ (2 r+5)^{3} $$ [D] $$ (2 r-10)\left(4 r^{2}+5 r+25\right) $$ $$ u^{3}-216 $$ [A] $$ (u-6)^{3} $$ [B] $$ (u-6)\left(u^{2}+36\right) $$ $$ [C](u-6)\left(u^{2}+6 u+36\right) $$ D] $$ (u+6)\left(u^{2}-6 u+36\right) $$ 6. $$ 27 d^{3}-64 $$ [A] $$ (3 d-4)\left(9 d^{2}+12 d+16\right) $$ [B] $$ (3 d+12)\left(9 d^{2}-4 d+16\right) $$ [C] $$ (3 d-4)^{3} $$ [D] $$ (3 d-4)\left(9 d^{2}+16\right) $$ 7. $$ c^{3}+8 $$ [A] $$ (c+2)\left(c^{2}+4\right) $$ [B] $$ (c-2)\left(c^{2}+2 c+4\right) $$ $$ [\mathrm{C}](c+2)\left(c^{2}-2 c+4\right) $$ [D] $$ (c+2)^{3} $$ 8. $$ 8 z^{3}+125 $$ [A] $$ (2 z+5)\left(4 z^{2}+25\right) $$ [B] $$ (2 z+5)^{3} $$ [C] $$ (2 z-10)\left(4 z^{2}+5 z+25\right) $$ [D] $$ (2 z+5)\left(4 z^{2}-10 z+25\right) $$ 9. $$ g^{3}-8 $$ $$ [\mathrm{A}](g-2)\left(g^{2}+4\right) $$ [B] $$ (g-2)^{3} $$ [C] $$ (g-2)\left(g^{2}+2 g+4\right) $$ [D] $$ (g+2)\left(g^{2}-2 g+4\right) $$ 10. $$ b^{3}+64 $$ $$ [A](b+4)\left(b^{2}-4 b+16\right) $$ [B] $$ (b+4)\left(b^{2}+16\right) $$ [C] $$ (b-4)\left(b^{2}+4 b+16\right) $$ [D] $$ (b+4)^{3} $$

Question

UpStudy AI · Accepted Answer

1. We have  
$$
m^3 + 27 = m^3 + 3^3.
$$  
Using the sum of cubes formula  
$$
a^3 + b^3 = (a+b)\left(a^2 - ab + b^2\right),
$$  
set $$a=m$$ and $$b=3$$. Then it factors as  
$$
(m+3)\left(m^2-3m+9\right).
$$  
Thus, the answer is [C].

2. We have  
$$
8b^3-125 = (2b)^3 - 5^3.
$$  
Using the difference of cubes formula  
$$
a^3-b^3=(a-b)\left(a^2+ab+b^2\right),
$$  
with $$a=2b$$ and $$b=5$$, we get  
$$
(2b-5)\left((2b)^2+2b\cdot5+5^2\right) = (2b-5)(4b^2+10b+25).
$$  
Thus, the answer is [A].

3. We have  
$$
27e^3-8 = (3e)^3-2^3.
$$  
Using the difference of cubes formula with $$a=3e$$ and $$b=2$$:  
$$
(3e-2)\left((3e)^2+3e\cdot2+2^2\right) = (3e-2)(9e^2+6e+4).
$$  
Thus, the answer is [C].

4. We have  
$$
8r^3+125 = (2r)^3+5^3.
$$  
Using the sum of cubes formula with $$a=2r$$ and $$b=5$$:  
$$
(2r+5)\left((2r)^2-2r\cdot5+5^2\right) = (2r+5)(4r^2-10r+25).
$$  
Thus, the answer is [B].

5. We have  
$$
u^3-216 = u^3-6^3.
$$  
Using the difference of cubes formula with $$a=u$$ and $$b=6$$:  
$$
(u-6)\left(u^2+6u+36\right).
$$  
Thus, the answer is [C].

6. We have  
$$
27d^3-64 = (3d)^3-4^3.
$$  
Using the difference of cubes formula with $$a=3d$$ and $$b=4$$:  
$$
(3d-4)\left((3d)^2+3d\cdot4+4^2\right) = (3d-4)(9d^2+12d+16).
$$  
Thus, the answer is [A].

7. We have  
$$
c^3+8 = c^3+2^3.
$$  
Using the sum of cubes formula with $$a=c$$ and $$b=2$$:  
$$
(c+2)\left(c^2-2c+4\right).
$$  
Thus, the answer is [C].

8. We have  
$$
8z^3+125 = (2z)^3+5^3.
$$  
Using the sum of cubes formula with $$a=2z$$ and $$b=5$$:  
$$
(2z+5)\left((2z)^2-2z\cdot5+5^2\right) = (2z+5)(4z^2-10z+25).
$$  
Thus, the answer is [D].

9. We have  
$$
g^3-8 = g^3-2^3.
$$  
Using the difference of cubes formula with $$a=g$$ and $$b=2$$:  
$$
(g-2)\left(g^2+2g+4\right).
$$  
Thus, the answer is [C].

10. We have  
$$
b^3+64 = b^3+4^3.
$$  
Using the sum of cubes formula with $$a=b$$ and $$b=4$$:  
$$
(b+4)\left(b^2-4b+16\right).
$$  
Thus, the answer is [A].
1. $$ (m+3)(m^2 - 3m + 9) $$ 2. $$ (2b - 5)(4b^2 + 10b + 25) $$ 3. $$ (3e - 2)(9e^2 + 6e + 4) $$ 4. $$ (2r + 5)(4r^2 - 10r + 25) $$ 5. $$ (u - 6)(u^2 + 6u + 36) $$ 6. $$ (3d - 4)(9d^2 + 12d + 16) $$ 7. $$ (c + 2)(c^2 - 2c + 4) $$ 8. $$ (2z + 5)(4z^2 - 10z + 25) $$ 9. $$ (g - 2)(g^2 + 2g + 4) $$ 10. $$ (b + 4)(b^2 - 4b + 16) $$

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