F.2 Factorization (MATHS)

Question

1) (4x²-9y²)-2x-3y

2) (x²-6x+9)-4y²

3) 9a²-(b²+26b+169)



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Answer 1

1.
(4x^ 2 - 9y^ 2) - 2x - 3y

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

= ( 2x + 3y) (2x - 3y - 1 )


2.
(x^ 2 - 6x + 9) - 4y^ 2

= ( x - 3) ^ 2 - (2y )^ 2

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

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

3.
9a^ 2 - (b^2 + 26b + 169)

= (3a)^ 2 - (b + 13)^ 2

= (3a + b + 13) (3a - b - 13)

Answer 2

<1>
( 4x² - 9y² ) - 2x - 3y
= [ (2x)² - (3y)² ] - ( 2x + 3y )
= ( 2x + 3y ) ( 2x - 3y ) - ( 2x + 3y )
= ( 2x + 3y ) ( 2x - 3y - 1 )

remark: a² - b² = ( a + b ) ( a - b )

<2>
( x² - 6x + 9 ) - 4y²
= ( x - 3 )² - (2y)²
= ( x - 3 + 2y ) ( x - 3 - 2y )

remark: a² - b² = ( a + b ) ( a - b ) & ( a - b )² = a² - 2ab + b²

<3>
9a² - ( b² + 26b + 169 )
= (3a)² - ( b + 13 )²
= ( 3a + b + 13 ) ( 3a - b -13 )

remark: a² - b² = ( a + b ) ( a - b ) & ( a - b )² = a² - 2ab + b²

Answer 3

1) (4x²-9y²)-2x-3y
=(2x)²-(3y)²-2x-3y
=(2x+3y)(2x-3y)-(2x+3y)
=(2x+3y)(2x-3y-1)

2) (x²-6x+9)-4y²
=(x-3)²-(2y)²
=(x-3+2y)(x-3-2y)

3) 9a²-(b²+26b+169)
=(3a)²-(b+13)²
=(3a+b+13)(3a-b-13)

以上用的方程式主要有:
a²-b²=(a+b)(a-b)
x²-ax+a²=(x-a)²
x²+ax+a²=(x+a)²