Question

Simplify: (3a + 5b)3 – (3a – 5b)3

Answer 1

Answer:

$\bf{(3a+5b)^3-(3a-5b)^3=(27a^2+25b^2)10b}$

$\text{Simplify: }(3a+5b)^3-(3a-5b)^3$

$\bf{(3a+5b)^3-(3a-5b)^3}$

$=[(3a)^3+(5b)^3+3*3a*5b(3a+5b)]-[(3a)^3+(-5b)^3+3*3a*(-5b)(3a-5b)]$

$=(3a)^3+(5b)^3+3*3a*5b(3a+5b)-(3a)^3-(-5b)^3-3*3a*(-5b)(3a-5b)$

$=(5b)^3+3*3a*5b(3a+5b)-(-5b)^3-3*3a*(-5b)(3a-5b)$

$=125b^3+45ab(3a+5b)-(-125b^3)+45ab(3a-5b)$

$=125b^3+45ab(3a+5b)+125b^3+45ab(3a-5b)$

$=125b^3+135a^2b+225ab^2+125b^3+135a^2b-225ab^2$

$=250b^3+270a^2b$

$=\bf{(27a^2+25b^2)10b}$

$\implies\:\bf{(3a+5b)^3-(3a-5b)^3=(27a^2+25b^2)10b}$

Answer 2

(3a+5b)

3

−(3a−5b)

3

=(27a

2

+25b

2

)10b

\text{Simplify: }(3a+5b)^3-(3a-5b)^3Simplify: (3a+5b)

3

−(3a−5b)

3

\bf{(3a+5b)^3-(3a-5b)^3}(3a+5b)

3

−(3a−5b)

3

=[(3a)^3+(5b)^3+3*3a*5b(3a+5b)]-[(3a)^3+(-5b)^3+3*3a*(-5b)(3a-5b)]=[(3a)

3

+(5b)

3

+3∗3a∗5b(3a+5b)]−[(3a)

3

+(−5b)

3

+3∗3a∗(−5b)(3a−5b)]

=(3a)^3+(5b)^3+3*3a*5b(3a+5b)-(3a)^3-(-5b)^3-3*3a*(-5b)(3a-5b)=(3a)

3

+(5b)

3

+3∗3a∗5b(3a+5b)−(3a)

3

−(−5b)

3

−3∗3a∗(−5b)(3a−5b)

=(5b)^3+3*3a*5b(3a+5b)-(-5b)^3-3*3a*(-5b)(3a-5b)=(5b)

3

+3∗3a∗5b(3a+5b)−(−5b)

3

−3∗3a∗(−5b)(3a−5b)

=125b^3+45ab(3a+5b)-(-125b^3)+45ab(3a-5b)=125b

3

+45ab(3a+5b)−(−125b

3

)+45ab(3a−5b)

=125b^3+45ab(3a+5b)+125b^3+45ab(3a-5b)=125b

3

+45ab(3a+5b)+125b

3

+45ab(3a−5b)

=125b^3+135a^2b+225ab^2+125b^3+135a^2b-225ab^2=125b

3

+135a

2

b+225ab

2

+125b

3

+135a

2

b−225ab

2

=250b^3+270a^2b=250b

3

+270a

2

b

=\bf{(27a^2+25b^2)10b}=(27a

2

+25b

2

)10b

\implies\:\bf{(3a+5b)^3-(3a-5b)^3=(27a^2+25b^2)10b}⟹(3a+5b)

3

−(3a−5b)

3

=(27a

2

+25b

2

)10b