Hi Tiff,

The first problem is to exand -3x times (x² + 2). When you multiply an algebraic quantity times the sum of two other quantities you need to multiply the first quantity by each of the other two and then add them. That is to multiply -3x times (x² + 2) you need to multiply -3x times x² and -3x times 2 and then add. Algebraically this is (I an going to use for multiplication)

-3x (x² + 2) = -3x x² + -3x 2

x times x² is x³ and -3 times 2 is -6 so this simplifies to

-3 x³ - 6x

The second problem is also an algebraic quantity (x+2) times the sum of two other quantities x and 3. Thus

(x+2) (x+3) = (x+2) x + (x+2) 3

But this can be written

x (x+2) + 3 (x+2)

Expand these two expressions the same way and then collect like terms.

Penny

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