factorise 75(x+y)² - 48(x-y)²
Answers
75(x+y)² - 48(x-y)²
Take out 3 as a common factor:
= 3 [ 25(x + y)² - 16(x - y)² ]
Write 25 as 5² and 16 as 4²:
= 3 [ 5²(x + y)² - 4²(x - y)² ]
Group them into a² - b²:
= 3 [ ( 5(x + y) )² - ( 4(x - y) )² ]
Apply a² - b² = (a + b) (a - b):
= 3 [ [5(x + y) + 4(x - y) ] [5(x + y) - 4(x - y) ] ]
Expand the terms in each bracket:
= 3 [ ( 5x + 5y + 4x - 4y) (5x + 5y - 4x + 4y) ]
Combine like terms:
= 3 ( 9x + y) (x + 9y )
Answer:
3 ( 9x + y) (x + 9y )
Step-by-step explanation:
75(x+y)² - 48(x-y)²
Take out 3 as a common factor:
= 3 [ 25(x + y)² - 16(x - y)² ]
Write 25 as 5² and 16 as 4²:
= 3 [ 5²(x + y)² - 4²(x - y)² ]
Group them into a² - b²:
= 3 [ ( 5(x + y) )² - ( 4(x - y) )² ]
Apply a² - b² = (a + b) (a - b):
= 3 [ [5(x + y) + 4(x - y) ] [5(x + y) - 4(x - y) ] ]
Expand the terms in each bracket:
= 3 [ ( 5x + 5y + 4x - 4y) (5x + 5y - 4x + 4y) ]
Combine like terms:
= 3 ( 9x + y) (x + 9y )
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