Expand (x+3)(2x+9)

(In terms of formatting, we'll use little x "x" to mean the algebraic variable, and big x "X" to mean multiply). When we see two sets of brackets written next to each other, such as (...)(...), this means that we need to multiply them together. When expanding brackets (i.e. multiplying them together), we need to multiply each element in the left-bracket, with each element in the right-bracket. [Be careful: we don't mutliply the elements in the left-bracket with other elements in the left-bracket, e.g. x and 3, or 2x and 9 (right)]. So, if we start with the first element in the left-bracket, x: 1) x X 2x = 2x^2 [Can you see why? When we multiply, we will get 2xx, which we can simplify as x^2 by collecting the x terms]. 2) x X 9 = 9x [Because we have 9 lots of x, i.e. 9x]. Now, if we do the second element in the right-bracket, 3: 1) 3 X 2x = 6x 2) 3 X 9 = 27 Now we have multiplied all our elements, we can simply add them together to give: (x+3)(2x+9)=2x^2 + 9x + 6x + 27 = 2x^2 + 15x + 27 This is expanded and simplified.