How do you find the product of ${(x + 5)}^{2}$ $(x + 5)^2$ ?

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How do you find the product of ${(x + 5)}^{2}$ $(x + 5)^2$ ?

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Answer 1 · 2018-03-20T03:05:20

$x^{2} + 10 x + 25$ $x^2 + 10x + 25$

Explanation:

We can use Binomial Expansion to find the product.

The Binomial Theorem States that,

For Any Integer $n > 0$ $n gt 0$ ,

${(x + y)}^{n} =$ $(x + y)^n =$ $(n$ $(n$ combination $0) x^{n} + (n$ $0)x^n + (n$ combination $1) x^{n - 1} y^{1}$ $1)x^(n-1)y^1$ + .............. + $(n$ $(n$ combination $n - 1) x^{1} y^{n - 1} + (n$ $n-1)x^1y^(n-1) + (n$ combination $n) y^{n}$ $n)y^n$

So, Here, use can use the formula.

${(x + 5)}^{2} =$ $(x + 5)^2 =$ $(2$ $(2$ combination $0) x^{2} + (2$ $0)x^2 + (2$ combination $1) x^{2 - 1} 5^{1}$ $1)x^(2-1)5^1$ + $(2$ $(2$ combination $1) x^{1} 5^{2 - 1} + (2$ $1)x^1 5^(2-1) + (2$ combination $2) 5^{2}$ $2)5^2$

= $1 \times x^{2} + 1 \times x \cdot 5 + 1 \times x \cdot 5 + 1 \times 5^{2}$ $1 xx x^2 + 1 xx x * 5 + 1 xx x* 5 + 1 xx 5^2$

[You should learn Permutations And Combinations Prior to this step.]

= $x^{2} + 5 x + 5 x + 25$ $x^2 + 5x + 5x + 25$

= $x^{2} + 10 x + 25$ $x^2 + 10x + 25$

Hope this helps.

Answer 2 · 2018-03-20T03:10:50

$x^{2} + 10 x + 25$ $x^2 + 10x + 25$

Explanation:

$\times {(x + 5)}^{2}$ $color(white)(xx)(x + 5)^2$

$= (x + 5) (x + 5)$ $= (x + 5)(x + 5)$ [Break it up]

$= x (x + 5) + 5 (x + 5)$ $= x(x + 5) + 5(x + 5)$ [Multiply]

$= (x^{2} + 5 x) + (5 x + 25)$ $= (x^2 + 5x) +(5x + 25)$ [Distributive Property]

$= x^{2} + 5 x + 5 x + 25$ $= x^2 + 5x + 5x + 25$

$= x^{2} + 10 x + 25$ $= x^2 + 10x + 25$ [Add everything up]

Hence Explained.

Answer 3 · 2018-03-20T03:13:09

FOIL(First, Outer, Inner, Last)
Answer: $x^{2} + 10 x + 25$ $x^2+10x+25$

Explanation:

${(x + 5)}^{2} = (x + 5) (x + 5)$ $(x+5)^2=(x+5)(x+5)$
First- Multiply $x \cdot x$ $x*x$ to get $x^{2}$ $x^2$
Outer- $x \cdot 5 = 5 x$ $x*5=5x$
Inner- $5 \cdot x = 5 x$ $5*x=5x$
Last- $5 \cdot 5 = 25$ $5*5=25$
We know have $x^{2} + 5 x + 5 x + 25$ $x^2+5x+5x+25$
$5 x + 5 x = 10 x$ $5x+5x=10x$
$x^{2} + 10 x + 25$ $x^2+10x+25$

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