Find the following products:(i) 6x/5(x3 + y3)(ii) xy (x3 – y3)(iii)

1.	Find the following products:(i) 6x/5(x3 + y3)(ii) xy (x3 – y3)(iii) 0.1y (0.1x5 + 0.1y)(iv) (-7/4ab2c – 6/25a2c2) (-50a2b2c2)
Answer» (i) 6x/5(x³ + y³) = 6/5x (x³ + y³) = (6/5x × x³) + (6/5x × y³) = 6/5x⁴ + 6/5xy³ (ii) xy (x³ – y³) = xy (x³ – y³) = (xy × x³) – (xy × y³) = x⁴y – xy⁴ (iii) 0.1y (0.1x⁵ + 0.1y) = 0.1y (0.1x5 + 0.1y) = (0.1y × 0.1x⁵) + (0.1y × 0.1y) = 0.01x⁵y + 0.01y² (iv) (-7/4ab²c – 6/25a²c²) (-50a²b²c²) = (-7/4ab²c – 6/25a²c²) (-50a²b²c²) = (-7/4ab²c × -50a²b²c²) – (6/25a²c² × -50a²b² × c²) = 350/4a³b⁴c³ + 12a⁴b²c⁴ = 175/2a³b⁴c³ + 12a⁴b²c⁴

Find the following products:(i) 6x/5(x3 + y3)(ii) xy (x3 – y3)(iii) 0.1y (0.1x5 + 0.1y)(iv) (-7/4ab2c – 6/25a2c2) (-50a2b2c2)

Answer»

(i) 6x/5(x³ + y³)

= 6/5x (x³ + y³)

= (6/5x × x³) + (6/5x × y³)

= 6/5x⁴ + 6/5xy³

(ii) xy (x³ – y³)

= xy (x³ – y³)

= (xy × x³) – (xy × y³)

= x⁴y – xy⁴

(iii) 0.1y (0.1x⁵ + 0.1y)

= 0.1y (0.1x5 + 0.1y)

= (0.1y × 0.1x⁵) + (0.1y × 0.1y)

= 0.01x⁵y + 0.01y²

(iv) (-7/4ab²c – 6/25a²c²) (-50a²b²c²)

= (-7/4ab²c – 6/25a²c²) (-50a²b²c²)

= (-7/4ab²c × -50a²b²c²) – (6/25a²c² × -50a²b² × c²)

= 350/4a³b⁴c³ + 12a⁴b²c⁴

= 175/2a³b⁴c³ + 12a⁴b²c⁴

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