Explanation

${x^}^2+18x+81=0$:

• The first term is x^2, so $a=x$.
• The last term is 81, so ${b^}^2=81$, which means $b=9$ (we take the positive root since the middle term is positive).
• The middle term is 18x. Let's check if it matches 2ab: $2(x)(9)=18x$. It does.

Therefore, the quadratic expression ${x^}^2+18x+81$ can be factored into $(x+9{)^}^2$.

So the factor form of the equation ${x^}^2+18x+81=0$ is $(x+9{)^}^2=0$.

Explanation

Given:
$x^2 - 3x - 10 = 0$

We are told that one factor is $(x - 5)$.
So, we divide the quadratic by $(x - 5)$ to find the other factor:

Method:
Use factoring:

We want two numbers that multiply to $-10$ and add to $-3$.
These numbers are -5 and 2.

Thus,

$$x^2 - 3x - 10 = (x - 5)(x + 2)$$

Explanation

Given:

5x + 8 = 23

Subtract 8 from both sides:

5x = 23 - 8

5x = 15

Divide both sides by 5:

x = 15 / 5

x = 3

Explanation

Given:

a - b = 4

ab = 5

The formula for a³ - b³ is:

a³ - b³ = (a - b)(a² + ab + b²)

We can also use the identity:

a³ - b³ = (a - b)³ + 3ab(a - b)

Substituting the given values:

a³ - b³ = (4)³ + 3 * 5 * 4

= 64 + 60

= 124

Explanation

Given:

1. 6x + 2y = 6300

2. 2x + y = 2600

Multiplying equation (2) by 2:

4x + 2y = 5200

Subtracting:

(6x + 2y) - (4x + 2y) = 6300 - 5200

2x = 1100

x = 550