Question

Simplify by method of factori
${z}^{2} - {8}^{2} + 15$
${z - 25}^{2}$
​

Answer 1

Correcting the given question :

We have to factorize the following -

1. z² - 8z + 15

2. z² - 25

1.

Now, z² - 8z + 15

[ here 15 can be written as 5 × 3 and 5 + 3 = 8 ]

= z² - (5 + 3) z + 15

= z² - 5z - 3z + 15

= z (z - 5) - 3 (z - 5)

[ taking (z - 5) common from both terms ]

= (z - 5) (z - 3)

This is the required factorization.

2.

Now, z² - 25

= z² - 5²

[ we use the formula: a² - b² = (a + b) (a - b) ]

= (z + 5) (z - 5)

This is the required factorization.

Answer 2

correct Question :

Factorize ;

$1) \: z {}^{2} - 8 {}^{2} + 15$

$2) \: z {}^{2} - 25$

Solution :

1) z² -8² +15

= z² -64 + 15

= z² -49

= z²- 7²

[use identity (a+b) (a-b) = a² - b²]

= (z+7) (z-7)

2) z² -25

= z² - 5 ²

[use identity (a+b) (a-b) = a² - b²]

= (z+5) (z-5)

___________________________

$\Large\boxed{\green{More \: Algebraic\: identies }}$

• ( a+b) ² = a² + b²+2ab

• ( a-b) ² = a² + b²- 2ab

if any doubt ask .