### Video Transcript

Expand 10 multiplied by three plus five 𝑏.

In order to expand any bracket, we need to distribute the number outside across the parentheses. This means that we need to multiply 10 by three and also 10 by five 𝑏. 10 multiplied by three is equal to 30. This means that the first term of our expansion is 30. 10 multiplied by five is equal to 50. Therefore, 10 multiplied by five 𝑏 is equal to 50𝑏. The second term of our expansion is 50𝑏. The expansion of 10 multiplied by three plus five 𝑏 is 30 plus 50𝑏.

We can check this answer by factorising or factoring our final expression. The highest common factor of 30 and 50 is 10. This means that we can take a 10 outside of the parentheses. 30 divided by 10 is equal to three. Therefore, the first term inside is three. 50 divided by 10 is equal to five. This means that 50𝑏 divided by 10 is equal to five 𝑏. The second term inside the parentheses is five 𝑏. As this is the same as the expression we started with, we know that our answer is correct.