Question

Multiply:

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

Answer 1

(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) $8\times \frac{1}{4}x$
$$\begin{gathered} =8\times \frac{1}{4}\times x \\ =\left(8\times \frac{1}{4}\right)\times x \\ =2x \end{gathered}$$

(6) $\frac{1}{2}{x}^2\times \frac{1}{3}{y}^2$
$$\begin{gathered} =\frac{1}{2}\times x\times x\times \frac{1}{3}\times y\times y \\ =\left(\frac{1}{2}\times \frac{1}{3}\right)\times \left(x\times x\right)\times \left(y\times y\right) \\ =\frac{1}{6}{x}^2{y}^2 \end{gathered}$$

(7) 3ax × 7a²x²
= 3 × a × x × 7 × a × a × x × x
= (3 × 7) × (a × a × a)×(x × x × x)
= 21a³x³

(8) $\frac{2}{3}{p}^2\times \frac{9}{4}{q}^3$
$$\begin{gathered} =\frac{2}{3}\times p\times p\times \frac{9}{4}\times q\times q\times q \\ =\left(\frac{2}{3}\times \frac{9}{4}\right)\times \left(p\times p\right)\times \left(q\times q\times q\right) \\ =\frac{3}{2}{p}^2{q}^3 \end{gathered}$$

(9) 7qy × 4rx
= 7 × q × y × 4 × r × x
= (7 × 4) × q × y × r × x
= 28qyrx

(10) $3x^{2}y\times \frac{5}{6}{x}^{2}y$
$$\begin{gathered} =3\times x\times x\times y\times \frac{5}{6}\times x\times x\times y \\ =\left(3\times \frac{5}{6}\right)\times \left(x\times x\times x\times x\right)\times \left(y\times y\right) \\ =\frac{5}{2}{x}^4{y}^2 \end{gathered}$$