Question

Simplify:-
1.
$(3a + b)^{3} + {(3a - b)}^{3}$
2.
${(3x + 2)}^{3} + {(3x - 2)}^{3}$
Best answer will be marked brainliest!!​

Answer 1

Step-by-step explanation:

3(4a−3b)(b−3a)(2b−a)

(4a−3b)

3

−(3a−b)

3

−(a−2b)

3

=(4a−3b)

3

+(b−3a)

3

+(2b−a)

3

Let,

x=4a−3b;y=b−3a;z=2b−a

On adding, x+y+z=0

∴x

3

+y

3

+z

3

=3xyz

Subtituting x, y, z values, we get

(4a−3b)

3

+(b−3a)

3

+(2b−a)

3

=3(4a−3b)(b−3a)(2b−a)

Answer 2

Step-by-step explanation:

Given:

1)$(3a + b)^{3} + {(3a - b)}^{3}$

2)${(3x + 2)}^{3} + {(3x - 2)}^{3}$

To find: Simplify

Solution:

Tip:

Identity used:

${(x + y)}^{3} = {x}^{3} + 3xy(x + y) + {y}^{3} \\ \\ {(x - y)}^{3} = {x}^{3} + 3xy(x - y) - {y}^{3}$

1) Apply these formulas

x=3a

y=b

${(3a + b)}^{3} + {(3a - b)}^{3}= {(3a)}^{3} + 3(3a)b(3a+b) + {b}^{3} + {(3a)}^{3} + 3(3a)b(3a-b) -{b}^{3}$$= 27{a}^{3} +27a^2b+9ab^2+b^3 + 27{a}^{3} +27a^2b-9ab^2-b^3$$=54a^3+54a^2b$$\bold{\red{{(3a + b)}^{3} + {(3a - b)}^{3}=54a^2(a+b)}}$

2) ${(3x + 2)}^{3} + {(3x - 2)}^{3}= {(3x)}^{3} + 3(3x)2(3x+2) + {(2)}^{3} + {(3x)}^{3} + 3(3x)2(3x-2) -{(2)}^{3}$$= 27{x}^{3} +54x^2+36x+8 + 27{x}^{3} +54x^2-36x-8$$=54x^3+108x^2$$\bold{\red{{(3x + 2)}^{3} + {(3x - 2)}^{3}=54x^2(x+2)}}$

Final answer:

${(3a + b)}^{3} + {(3a - b)}^{3}=54a^2(a+b)\\ \\ {(3x + 2)}^{3} + {(3x - 2)}^{3}=54x^2(x+2)$

Hope it helps you.