Question

Factorise :-
i)x² + xy + 8 x + 8y
ii) p²- 10 p +25
iii) 63 a² - 112b²
iv) p²+6p - 16
v) 27 x³ + 64y³ - 125z³ + 180 xyz
Please help i will mark him or her as brainleast answer please..its my promise as soon as possible..
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Answer 1

Given :-

It is given to factorise the given expression;

• x² + xy + 8x + 8y
• p² - 10p + 25
• 63a² - 112b²
• p² + 6p - 16
• 27x³ + 64y³ - 125z³ + 180xyz

Solution :-

Here's the factorization for the given expressions;

• x² + xy + 8x + 8y

⇒ x² + xy + 8x + 8y

⇒ x(x + y) + 8(x + y)

⇒ (x + y)(x + 8)

• p² - 10p + 25

⇒ p² - 10p + 25

⇒ p(p - 5) - 5(p - 5)

⇒ (p - 5)(p - 5)

⇒ (p - 5)²

• 63a² - 112b²

⇒ 63a² - 112b²

⇒ 7(9a² - 16b²)

⇒ (3a - 4b)(3a + 4b)

⇒ 7(3a - 4b)(3a + 4b)

• p² + 6p - 16

⇒ p² + 6p - 16

⇒ (p² - 2p) + (8p - 16)

⇒ p(p - 2) + 8(p - 2)

⇒ (p - 2)(p + 8)

• 27x³ + 64y³ - 125z³ + 180xyz

⇒ 27x³ + 64y³ - 125z³ + 180xyz

⇒ 27x³ + 180yzx + 64y³ - 125z³

⇒ (3x + 4y - 5z)(9x² - 12xy + 15xz + 16y² + 20yz + 25z²)

Thanks!!! :D

Answer 2

$\sf\huge\bold{Answer:}$

Given :

i)x² + xy + 8 x + 8y

ii) p²- 10 p +25

iii) 63 a² - 112b²

iv) p²+6p - 16

v) 27 x³ + 64y³ - 125z³ + 180 xyz

To find :

Factors of each part.

Solution :

$\fbox{part i) }$

$⇒ \: x² + xy + 8 x + 8y \\ ⟶x(x + y) + 8(x + y) \\ ⟶(x + y)(x + 8)$

$\fbox{part ii) }$

$⇒p²- 10 p +25 \\ ⟶ {p}^{2} - 5p - 5p + 25(splitting \: middle \: term)\\ ⟶( {p}^{2} - 5p) + ( - 5p + 25) \\ ⟶p(p - 5) - 5(p - 5) \\ ⟶( p- 5)( p- 5) \\ or \: ⟶{(p - 5)}^{2}$

$\fbox{part iii) }$

$⇒ 63 a² - 112b² \\ ⟶7(9 {a}^{2} - 16 {b}^{2}) \\ ⟶7( {(3a)}^{2} - {(4b)}^{2})$

Using identity a² - b² = (a-b)(a+b)

$⟶7(3a - 4b)(3a + 4b)$

$\fbox{part iv) }$

$⇒p²+6p - 16 \\ ⟶ {p}^{2} + 8p - 2p - 16(splitting \: middle \: term) \\ ⟶( {p}^{2} + 8p) + ( - 2p - 16)\\ ⟶p(p + 8) - 2(p + 8) \\ ⟶( p+ 8)(p - 2)$

$\fbox{part v) }$

$⇒27 x³ + 64y³ - 125z³ + 180 xyz \\ ⟶27 x³ + 64y³ - 125z³ -180xyz\\⟶(3x+4y-5z)(9x²-12xy+15xz+16y²+20yz+25z²$