Factor the following, otherwise write prime

Question

1) x^4-6x^2+27

2) 12x^2+16x-35

3) 2(a+b)^2-4(a+b)

4) 162a^2+144ab+32b^2

Answer 1

1)

x⁴ - 6x² + 27

= (x²)² - 6x² + 27

= (x²)² - 9x² + 3x² + 27

= x² ( x² - 9 ) + 3 ( x² + 9 )

No Common term exist here.So No real factors exist.

Solution : PRIME

Answer 2

2)

12x²+16x-35

= 12x² + 30x - 14x – 35

= 12x² + 30x - 14x - 35

= 6x ( 2x +5) – 7 ( 2x +5)

= ( 2x +5) (  6x – 7 )

Solution : Factor Form is  ( 2x + 5) ( 6x – 7 ) .

Answer 3

3)

2(a+b)²-4(a+b)

Take out common factor 2(a+b).

[ 2(a+b) ] [ (a+b) - 2 ]

Solution : Factor Form is  [ 2(a+b) ] [ (a+b) - 2 ].

Comments

How do you get -2 for [a+b)-2]

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= 2(a+b)² - 4(a+b)

= 2(a+b)(a+b) - 2*2(a+b)

= 2(a+b)*(a+b) - 2*2(a+b)

When you take out 2(a+b) as common factor.

(a+b) will be remained in first term 2(a+b)*(a+b).

-2 will be remained in second term  -2*2(a+b).

Then

= [2(a+b)]  [ (a+b) - 2 ]

Answer 4

4)

162a² + 144ab + 32b²

= 2( 81a² + 72ab + 16b² )

= 2 ( 81a² + 36ab + 36ab + 16b² )

= 2 [ 9a( 9a + 4b ) + 4b( 9a + 4b ) ]

= 2 [ ( 9a + 4b ) ( 9a + 4b ) ]

= 2 (9a + 4b)²

Solution : Factor Form is  2 (9a + 4b)².