please find the answer
Answers
Important formulas :
- ( a + b )( a - b ) = a² - b²
- ( a + b )² = a² + b² + 2 ab
- ( a - b )² = a² + b² - 2 ab
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(a) ( a - b )² - ( b - c )²
==> a² + b² - 2 ab - b² - c² + 2 bc
==> a² - c² - 2 ab - 2 bc
==> a² - c² - 2 b ( a - c )
==> ( a + c )( a - c ) - 2 b ( a - c )
==> ( a - c )( a + c - 2 b )
(b) 64 - 25 x²+60 x y - 36 y²
==> 64 - ( 5 x)² - ( 6 y )² + 2 . 5x. 6y
==> 64 - ( 5 x - 6 y )²
==> 8² - ( 5 x - 6 y )²
==> ( 8 - 5 x + 6 y )( 8 + 5 x - 6 y )
(c) x⁴ - 1
==> (x²)² - 1²
==> ( x² - 1 )( x² + 1 )
==> ( x + 1 )( x - 1 )( x² + 1)
(d) (x - 2 y )² - ( 2 x + y )²
==> ( x - 2 y - 2 x - y )( x - 2 y + 2 x + y )
==> ( - x - 3 y )( 3 x - y )
==> - ( x + 3 y )( 3 x - y )
(e) 36 x² - 49 ( y - x )²
==> ( 6 x)² - [ 7 ( y - x ) ]²
==> ( 6 x - 7 ( y - x ) ) ( 6 x + 7 ( y - x ))
==> ( 6 x + 7 x - 7 y )( 7 y - x )
==> ( 13 x - 7 y )( 7 y - x )
(f) ( p + q )² - 81
==> ( p + q )² - 9²
==> ( p + q - 9 )( p + q + 9 )
(g) 4 p² - 12 p q + 9 q² - 64
==> ( 2 p)² - 2.2p.3q + ( 3 q)² - 64
==> ( 2 p - 3 q )² - 8²
==> ( 2 p - 3 q + 8 )( 2 p - 3 q - 8 )
(h) ( 4 b - 3 c )² - ( 3 b + 2 c )²
==> ( 4 b - 3 c - 3 b - 2 c ) ( 4 b - 3 c + 3 b + 2 c )
==> ( b - 5 c )( 7 b - c )
(i) c² - a² - b² - 2 ab
==> c² - ( a + b )²
==> ( c - a - b )( c + a + b )
Hope it helps u ^___^
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