Question

Factorize using suitable identies....
i.) (p + 10)(p +11)
ii.) (4x + 9)(4x + 12)
iii.) (x - 5)(x - 1)
iv.)(9x - 5)(9x -1)
v.)(2x + 5y)(2x + 3y)

Answer 1

★ Solution :

Using identity = x² + (a + b) x + ab

❶ (p + 10) ( p + 11)

➛p² + (10 + 11) × x + (10 × 11)

➛p² + 21x + 110

__________

❷ (4x + 9)(4x + 12)

➛4x² + (9 + 12) × 4x + (9 × 12)

➛16x² + 48x + 108

__________

❸ (x - 5)(x - 1)

➛x² + (5 + 1) × x + ( 5 × 1)

➛x² + 6x + 5

__________

❹ (9x - 5)(9x -1)

➛9x² + (5 + 1) × 9x + (5 × 1)

➛81x² + 54x + 5

___________

❺ (2x + 5y)(2x + 3y)

➛2x² + (5y + 3y) × 2x + (5y × 3y)

➛4x² + 16xy + 15y²

___________

Answer 2

Answers :

¡) p² + 21x + 110

¡¡) 16x² + 48x + 108

¡¡¡) x² - 6x + 5

iv) 81x² - 54x + 5

v) 4x² + 16xy + 15y²

Solutions :

Using identity :

$\red\bigstar\large\boxed{\tt (x+a)(x+b) = x^2 + (a + b) x + ab}$

Now Apply this identity here,

$\large \sf i) \color{green}{(p + 10) ( p + 11)}$

➩ p² + (10 + 11)x + (10 × 11)

➩ p² + 21(x) + 110

➩ p² + 21x + 110

━━━━━━━━━━━━━━━

$\large\sf ii) \color{green}{(4x + 9)(4x + 12)}$

➩ (4x)² + (9 + 12)(4x) + (9 × 12)

➩ 16x² + 21(4x) + 108

➩ 16x² + 84x + 108

━━━━━━━━━━━━━━━

$\large\sf iii) \color{green}{(x - 5)(x - 1)}$

➩ x² + (-5 - 1)x + ( -5 × -1)

➩ x² +(-6)x + (5)

➩ x² - 6x + 5

━━━━━━━━━━━━━━━

$\large\sf iv) \color{green}{(9x - 5)(9x -1)}$

➩ (9x)² + (-5 -1)(9x) + (-5 × -1)

➩ 81x² +(-6)(9x) + (5)

➩ 81x² - 54x + 5

━━━━━━━━━━━━━━━

$\large \sf v) \sf \color{green}{(2x + 5y)(2x + 3y)}$

➩ (2x)² + (5y + 3y)(2x) + (5y × 3y)

➩ 4x² + [10xy + 6xy ] + 15y²

➩ 4x² + 16xy + 15y²

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