Question

`\huge\text{\bold{Question:}}`

Could anyone please help me with my homework? Thanks in advance! :)

`\huge\bold{(x+2)^(3) }`
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Answer 1

Given:

`(x + 2)^(3)`

Now using algebraic identities,

`{x}^(3) + 3(x)^(2) + 3(x)(2)^(2) + {2}^(3)`

`= > {x}^(3) + 3(x)^(2) + 3(x)(2)^(2) +8`

`= > {x}^(3) + 6x^(2) +12x +8`

~ Benjemin360

Answer 2

• Before you solve this question, remember this identity of the cube of a binomial.

`(a + b) ^(3) = {a}^(3) + {b}^(3) + 3ab(a + b) \\`

• Here, we have to find the cube of (x + 2).
• Replacing a by x and b by 2 in the above identity, we have

`(x + 2) ^(3) \\ = {(x)}^(3) + (2) ^(3) + 3 * x * 2(x + 2) \\ = {x}^(3) + 8 + 6x(x + 2) \\ = {x}^(3) + 8 + 6x * x + 6x * 2 \\ = {x}^(3) + 8 + {6x}^(2) + 12x`

• Now, arrange the above expression in standard form.

`= {x}^(3) + {6x}^(2) + 12x + 8 \\`

Answer:

`{x}^(3) + {6x}^(2) + 12x + 8`

Hope you could understand.

If you have any query, feel free to ask.