Question

Factorise the following expressions: a) 14w + 21 b) 27x+18​

Answer 1

Hi!

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$\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup$

#1 7(2w+3)

#2 9(3x+2)

$\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup$

We need to factor these two expressions.

$\twoheadrightarrow\sf 14w+21$ and $\twoheadrightarrow\sf 27x+18$

For now let's focus on the first expression.

Note that both terms, 14w and 21, have something in common.

In fact, they have 7 in common. So we factor it out by dividing 14w and 21 by 7.

$\twoheadrightarrow\sf14w\div7=2x\\\twoheadrightarrow\sf21\div7=3$

$\bullet$ Put the terms together, with a plus sign in between since they are positive

$\twoheadrightarrow\sf 2w+3$

$\bullet$ Put parentheses around 2w+3

$\twoheadrightarrow\sf (2w+3)$

$\bullet$ Put7 outside the parentheses

$\twoheadrightarrow\sf7(2w+3)$

$\bullet$ Great job! We factored the expression

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This problem can be solved the same way!

This time, both terms have a 9 in common.

$\twoheadrightarrow\sf 27x+18$

So we divide both terms by 9.

$\twoheadrightarrow\sf 27x\div9=3x\\\twoheadrightarrow\sf18\div9=2$

$\bullet$ Put the terms together, with a plus sign in between since they're positive

$\twoheadrightarrow\sf 3x+2$

$\bullet$ Next, put parentheses around 3x+2 and put 9 outside the parentheses

$\twoheadrightarrow\sf 9(3x+2)$

$\bullet$ Great job! We factored both expressions

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Hope that this helped! Best wishes.

$\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}$

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Answer 2

Step-by-step explanation:

a) 14w + 21

- Factor out 7 from the expression

7 (2w + 3)

b) 27x + 18

- Factor out 9 from the expression

9 (3x + 2)