Question

factorize the following using identities and midterm breaking where applicable;
a.(4p-3q)2
b.(a+1/4) (a-1/4)
c.y2 +5y+6
2 in every Q is square

Answer 1

The given equation is

⇒3y=y+2

⇒3y−y=2

⇒2y=2

⇒y=

2

2

=1

Then the value of 2y=2×1=2

Answer 2

Correct Question

• (4p - 3q)²
• (a + ¼)(a - ¼)
• y² - 5y + 6

Solution

• (4p - 3q)²

★ Apply identity :

(a - b)² = a² + b² - 2ab

→ (4p)² + (3q)² - 2 × 4p × 3q

→ 16p² + 9q² - 24pq

_____________________

• (a + ¼)(a - ¼)

★ Apply identity

a² - b² = (a + b)(a - b)

→ (a)² - (½)²

→ a² - ½

_____________________

• y² - 5y + 6

★ splitting middle term

→ y² - 6y - y + 6

→ y(y - 6) - 1(y - 6)

→ (y - 6)(y -1)

_____________________

Some Identities

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