Question

factorise: - 4x²+9y²+16z²+12xy-24yz-16xz plz help​

Answer 1

Answer:

2x + 3y - 4z) (2x + 3y - 4z)

Step-by-step explanation:

4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 16xz

We use this identity here...

(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 16xz

= (2x)^2 + (3y)^2 + (4y)^2 + 2 × 2x × 3y + 2 × 3y × (-4y) + 2 × 2x × (-4y)

= (2x + 3y - 4z)^2

= (2x + 3y - 4z) (2x + 3y - 4z)

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Answer 2

Question :

Factorise: - 4x²+9y²+16z²+12xy-24yz-16xz.

SoIution :

Let's start with what is given ; factorize :

⇒ 4x² + 9y² + 16z² + 12xy - 24yz - 16xz

Now comparing that with the identity :

⇔ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Now we get :

⇒ 4x² + 9y² + 16z² + 12xy - 24yz - 16xz

⇒ (2x)² + (3y)² + (-4z)² + 2 × 2x × 3y + 2 × 3y × (-4z) + 2 × (-4z) × 2x

⇒ [2x + 3y + (-4z)]²

⇒ [2x + 3y - 4z]²

⇒ (2x + 3y - 4z) (2x + 3y - 4z)

∴ Required answer = (2x + 3y - 4z) (2x + 3y - 4z)

More identities :

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• (a + b)² = (a - b)² + 4ab
• (a - b)² = (a + b)² - 4ab
• a³ + b³ = (a + b)³ - 3ab(a + b)
• a³ - b³ = (a - b)³ + 3ab(a - b)