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

Solution:

• 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

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

• 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.

Answer 2

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