Question

Factorise 9w² - 100​

Answer 1

Answer:

$9\, w^{2} - 100 = (3\, w - 10) \, (3\, w + 10)$.

Step-by-step explanation:

Fact:

$\begin{aligned} & (a - b)\, (a + b)\\ =\; & a^{2} + a\, b - a\, b - b^{2} \\ =\; & a^{2} - b^{2} \end{aligned}$.

In other words, $(a^{2} - b^{2})$, the difference of two squares in the form $a^{2}$ and $b^{2}$, could be factorized into $(a - b)\, (a + b)$.

In this question, the expression $(9\, w^{2} - 100)$ is the difference between two terms: $9\, w^{2}$ and $100$.

• $9\, w^{2}$ is the square of $3\, w$. That is: $(3\, w)^{2} = 9\, w^{2}$.
• On the other hand, $10^{2} = 100$.

Hence:

$9\, w^{2} - 100 = (3\, w)^{2} - (10)^{2}$.

Apply the fact that $a^{2} - b^{2} = (a - b) \, (a + b)$ to factorize this expression. (In this case, $a = 3\, w$ whereas $b = 10$.)

$\begin{aligned}& 9\, w^{2} - 100 \\ =\; & (3\, w)^{2} - (10)^{2} \\ = \; & (3\, w - 10)\, (3\, w + 10)\end{aligned}$.