Question

# Multiply: (1) 4x × 6y (2) 3a × 8b (3) 2x2 ×7x (4) 7x3 × 9 (5) $8×\frac{1}{4}x$ (6) $\frac{1}{2}{x}^{2}×\frac{1}{3}{y}^{2}$ (7) 3ax × 7a2x2 (8) $\frac{2}{3}{p}^{2}×\frac{9}{4}{q}^{3}$ (9) 7qy × 4rx (10) $3{x}^{2}y×\frac{5}{6}{x}^{2}y$

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Solution

## (1) 4x × 6y = 4 × x × 6 × y = (4 × 6) × x × y = 24xy (2) 3a × 8b = 3 × a × 8 × b = (3 × 8) × a × b = 24ab (3) 2x2 × 7x = 2 × x × x × 7 × x = (2 × 7) × (x × x × x) = 14x3 (4) 7x3 × 9 = 7 × x × x × x × 9 = (7 × 9) × (x × x × x) = 63x3 (5) $8×\frac{1}{4}x$ $=8×\frac{1}{4}×x\phantom{\rule{0ex}{0ex}}=\left(8×\frac{1}{4}\right)×x\phantom{\rule{0ex}{0ex}}=2x$ (6) $\frac{1}{2}{x}^{2}×\frac{1}{3}{y}^{2}$ $=\frac{1}{2}×x×x×\frac{1}{3}×y×y\phantom{\rule{0ex}{0ex}}=\left(\frac{1}{2}×\frac{1}{3}\right)×\left(x×x\right)×\left(y×y\right)\phantom{\rule{0ex}{0ex}}=\frac{1}{6}{x}^{2}{y}^{2}$ (7) 3ax × 7a2x2 = 3 × a × x × 7 × a × a × x × x = (3 × 7) × (a × a × a)×(x × x × x) = 21a3x3 (8) $\frac{2}{3}{p}^{2}×\frac{9}{4}{q}^{3}$ $=\frac{2}{3}×p×p×\frac{9}{4}×q×q×q\phantom{\rule{0ex}{0ex}}=\left(\frac{2}{3}×\frac{9}{4}\right)×\left(p×p\right)×\left(q×q×q\right)\phantom{\rule{0ex}{0ex}}=\frac{3}{2}{p}^{2}{q}^{3}$ (9) 7qy × 4rx = 7 × q × y × 4 × r × x = (7 × 4) × q × y × r × x = 28qyrx (10) $3{x}^{2}y×\frac{5}{6}{x}^{2}y\phantom{\rule{0ex}{0ex}}$ $=3×x×x×y×\frac{5}{6}×x×x×y\phantom{\rule{0ex}{0ex}}=\left(3×\frac{5}{6}\right)×\left(x×x×x×x\right)×\left(y×y\right)\phantom{\rule{0ex}{0ex}}=\frac{5}{2}{x}^{4}{y}^{2}$

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