Fill in the gaps to factorise this expression
[tex]$18 t+9=9(\ldots+\ldots)$[/tex]
Answer (1)
Divide each term of the expression by 9.
18 t /9 = 2 t .
9/9 = 1 .
The factorised expression is 9 ( 2 t + 1 ) .
Explanation
Understanding the Problem We are given the expression 18 t + 9 and we want to factorise it in the form 9 ( ⋯ + … ) . This means we want to find what to put inside the parentheses so that when we multiply it by 9, we get the original expression.
Finding the Missing Terms To find the missing terms, we can divide each term in the original expression by 9. So, we need to calculate 18 t /9 and 9/9 .
Calculating the First Term Let's calculate 18 t /9 . Since 18/9 = 2 , we have 18 t /9 = 2 t .
Calculating the Second Term Now let's calculate 9/9 . This is simply equal to 1.
Final Factorised Expression So, the factorised expression is 9 ( 2 t + 1 ) . Therefore, the missing terms are 2 t and 1 .
The Answer Thus, we have 18 t + 9 = 9 ( 2 t + 1 ) .
Examples
Factoring is a useful skill in algebra. For example, if you are trying to solve the equation 18 t + 9 = 0 , you can factor the left side as 9 ( 2 t + 1 ) = 0 . Then, since 9 is not 0, you must have 2 t + 1 = 0 . Solving for t , you get 2 t = − 1 , so t = − 2 1 . Factoring simplifies the process of solving equations.
