Question

Factorising and making m the subject of...

Answer 1

see explanation

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 =
`(g-5)/(a+3)`

Answer 2

a)

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

b) g - 3m = am + 5

am + 3m = 5 - g

m (a + 3) = 5 - g

m =

`(5 - g)/(a + 3)`

Explanation:

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