Question

By using standard formulae,expand 〖(x+2)〗^3.

Answer 1

$\rule{300}2$

Correct Question:

expand (x+2)³

$\rule{300}2$

Your Answer:

The standard Formula of finding the cube of sum of two variables is

• (x+y)³=x³+y³+3xy(x+y)

So,

(x+2)³

=x³ + 2³ + 3(x)(2)(x+2)

=x³ + 8 + 6x(x+2)

=x³ + 8 + 6x² +12x

=x³ + 6x² + 12x + 8

So, the expanded form of (x+2)³ is x³+6x²+12x+8

$\rule{300}2$

Additional:

The another Formula two find the cube of sum of two variable is

• (x+y)³=x³+y³+3x²y+3xy²

Some, other formulas are

• (x+y)²=x²+y²+2xy
• (x-y)²= x²+y²-2xy
• (x+a)(x+b)= x²+(a+b)x+ab
• x³+y³=(x+y)(x²+y²-xy)
• x³-y³=(x-y)(x²+y²+xy)

Concept used:-

• Multiplication of numbers
• Addition of Numbers
• Cubing of Number
• Opening of Brackets
• Algebraic Identities

$\rule{300}2$

Answer 2

✯✯ QUESTION ✯✯

Expand ( x + 2 )³..

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\longmapsto\tt{{(x+2)}^{3}}$

☛Using Identity : -

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

☛Putting Values : -

$\longmapsto\tt{{x}^{3}+{2}^{3}+3(x)(2)(x+2)}$

$\longmapsto\tt{{x}^{3}+8+6x(x+2)}$

$\longmapsto\tt{{x}^{3}+8+{6x}^{2}+12x}$

$\longmapsto\tt{{x}^{3}+{6x}^{2}+12x+8}$

_______________________

➥Some More Identities : -

★(x+y)²=x²+2xy+y²

★(x-y)²=x²-2xy+y²

★x²-y²=(x+y)(x-y)

★(x+a) (x+b) = x²+(a+b)x+ab

★(x - y)³= x³ + y³ +3xy (x+y)

★(x - y)³= x³ + y³ +3xy (x+y)

★x³ + y³ + z³- 3xyz = (x+y+z) (x²+y²+z²-xy-yz-zx)