Question

Factorising and making m the subject of...

Answer 1

Answer:

a)

$4x {}^{2} - 9 = (2x + 3)(2x - 3)$

b) g - 3m = am + 5

am + 3m = 5 - g

m (a + 3) = 5 - g

m =

$\frac{5 - g}{a + 3}$

Step-by-step explanation:

$a {}^{2} - b {}^{2} = (a + b)(a - b)$

Answer 2

Answer:

see explanation

Step-by-step explanation:

(a)

4x² - 9 ← is a difference of squares which factors in general as

a² - b² = (a + b)(a - b)

4x² = (2x)² ⇒ a = 2x and 9 = 3² ⇒ b = 3, thus

4x² - 9 = (2x + 3)(2x - 3)

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(b)

g - 3m = am + 5 ( collect the terms in m together )

Add 3m to both sides

g = am + 3m + 5 ( subtract 5 from both sides )

g - 5 = am + 3m ← factor out m from each term

g - 5 = m(a + 3) ← divide both sides by (a + 3)

m = $\frac{g-5}{a+3}$