Factorize (4a+3)^2 -(3a-2)^2?
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Remark:
m² - n² = ( m - n ) ( m + n )
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( 4 a + 3 )² - ( 3 a - 2 )² = [ ( 4 a + 3 ) - ( 3 a - 2 ) ] ∙ [ ( 4 a + 3 ) + ( 3 a - 2 ) ] =
( 4 a + 3 - 3 a + 2 ) ∙ ( 4 a + 3 + 3 a - 2 ) = ( a + 5 ) ∙ ( 7 a + 1 )
To factorize the expression (4a+3)^2 - (3a-2)^2, we can use the difference of squares formula.
The difference of squares formula states that for any two perfect squares, say (x+y)^2 - (x-y)^2, it can be factorized as (x+y+x-y)(x+y-x+y), which simplifies to (2x)(2y), which further simplifies to 4xy.
Applying this formula to our expression, we have:
(4a+3)^2 - (3a-2)^2 = [(4a+3) + (3a-2)][(4a+3) - (3a-2)]
Expanding this further:
= [(4a+3) + (3a-2)] [(4a+3) - (3a-2)]
= [4a + 3 + 3a - 2][4a + 3 - 3a + 2]
= (7a + 1)(a + 5)
So, the factored form of (4a+3)^2 - (3a-2)^2 is (7a + 1)(a + 5).