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/7=2x\\\twoheadrightarrow\sf21/7=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/9=3x\\\twoheadrightarrow\sf18/9=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

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)