Question

# Factorise: $$36{ \left( 5x+y \right) }^{ 2 }-25{ \left( 4x-y \right) }^{ 2 }$$

Solution

## We know that $$a^2-b^2=(a+b)(a-b)$$ Using the above identity, the Expression $$36(5x+y)^2-25(4x-y)^2$$ can be factorised as follows:$$36(5x+y)^2-25(4x-y)^2=(6(5x+y))^2-(5(4x-y))^2=[6(5x+y)-5(4x-y)][6(5x+y)+5(4x-y)]$$$$=(30x+6y-20x+5y)(30x+6y+20x-5y)=(10x+11y)(50x+y)$$Hence, $$36(5x+y)^2-25(4x-y)^2=(10x+11y)(50x+y)$$Mathematics

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