Question

Factories
1. (x-3)^2 - 36
2. 4x^2-9

Answer 1

Answer:

1. ( x + 3 ) ( x - 9 )
2. ( 2x + 3 ) ( 2x - 3 )

Step-by-step explanation:

1. (x-3)^2 - 36

= x² - 6x + 9 - 36

= x² - 6x - 27

by middle term splitting ,

sum = -6 = -9 + 3

product = -27 = -9 × 3

= x² - 9x + 3x - 27

= x ( x - 9 ) + 3 ( x - 9 )

= ( x + 3 ) ( x - 9 )

2. 4x^2-9

= 4x² + 0x - 9

by middle term splitting ,

sum = 0 = -6 + 6

product = -36 = -6 × 6

= 4x² - 6x + 6x - 9

= 2x ( 2x - 3 ) + 3 ( 2x - 3 )

= ( 2x + 3 ) ( 2x - 3 )

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Answer 2

Answer:

Question :-

1. (x - 3)² - 36

Answer :-

➠ (x - 3)² - 36

➻ (x)² - 2 × x × 3 + (3)² - 36 [(a - b)² = a² - 2ab + b² ]

➻ x² - 6x + 9 - 36

➻ x² - 6x - 27

➻ x² - (9 - 3)x - 27

➻ x² - 9x + 3x - 27

➻ x(x - 9) + 3(x - 9)

➻ (x - 9) (x + 3)

Question :-

2. 4x² - 9

Answer :-

➠ 4x² - 9

➻ (2x)² - (3)² [ (a)² - (b)² = (a + b) (a - b) ]

➻ (2x + 3) (2x - 3)