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To simplify the expression (3 \times 6(w + 4) \times w), first multiply (3) and (6) to get (18). Then, distribute (w) inside the parentheses: (18(w + 4)w = 18(w^2 + 4w)). Thus, the simplified expression is (18w^2 + 72w).
For the first rectangle, (L x W) = (5 x W) = 15, so W = 3 cm.The second rectangle is included in the question just to confuse you.
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She can use any letter (or symbol) that she wants to. Since w is the first letter of width, it seems like a good choice.
To factor 4w^2 + 12w + 4 = 0, first divide the equation by 4 to simplify it: w^2 + 3w + 1 = 0. Then, decompose the middle term (3w) into two terms whose product is the product of the coefficient of w^2 and the constant term (1): (w+1)(w+1) = 0. Therefore, the factors are (w+1)(w+1) = 0.