Expand the following products. (i) (3 + u)(v - 3) (ii) 2/3(15 + 6a) (iii) (10a + b)(10c + d) (iv) (3 - x)(x - 6) (v) (-5a + b)(c + d) (vi) (5 + z)(y + 9)

(i) 3v - 9 + uv - 3u (ii) 10 + 4a (iii) 100ac + 10ad + 10bc + bd (iv) -x² + 9x - 18 (v) -5ac - 5ad + bc + bd (vi) 5y + 45 + zy + 9z — (i) Apply distributive property: 3 × v + 3 × (-3) + u × v + u × (-3) = 3v - 9 + uv - 3u (ii) Distribute: 2/3 × 15 + 2/3 × 6a = 10 + 4a (iii) Each term multiplies each term: 10a × 10c + 10a × d + b × 10c + b × d (iv) Expand: 3x - 18 - x² + 6x = -x² + 9x - 18 (v) Distribute: -5a × c + (-5a) × d + b × c + b × d (vi) Expand: 5y + 45 + zy + 9z

Expand the following products. (i) (3 + u)(v - 3) (ii) 2/3(15 + 6a)… — Mathematics Part 1

Question 1 of 27intermediate🔧 ApplyNumerical6 marks

Expand the following products. (i) $(3 + u)(v - 3)$ (ii) $\frac{2}{3}(15 + 6a)$ (iii) $(10a + b)(10c + d)$ (iv) $(3 - x)(x - 6)$ (v) $(-5a + b)(c + d)$ (vi) $(5 + z)(y + 9)$

(i)

Answer

$3v - 9 + uv - 3u$

(ii)

Answer

$10 + 4a$

(iii)

Answer

$100ac + 10ad + 10bc + bd$

(iv)

Answer

$-x^2 + 9x - 18$

(v)

Answer

$-5ac - 5ad + bc + bd$

(vi)

Answer

$5y + 45 + zy + 9z$

Explanation

(i) Apply distributive property: $3 \times v + 3 \times (-3) + u \times v + u \times (-3) = 3v - 9 + uv - 3u$ (ii) Distribute: $\frac{2}{3} \times 15 + \frac{2}{3} \times 6a = 10 + 4a$ (iii) Each term multiplies each term: $10a \times 10c + 10a \times d + b \times 10c + b \times d$ (iv) Expand: $3x - 18 - x^2 + 6x = -x^2 + 9x - 18$ (v) Distribute: $-5a \times c + (-5a) \times d + b \times c + b \times d$ (vi) Expand: $5y + 45 + zy + 9z$