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Question

Show that: $$(3x+ 7)^2-84x=(3x-7)^2$$


Solution

LHS $$= (3x + 7)^2 -84x$$

Using , $$(a +b)^2 = a^2 +2ab + b^2$$

$$= (9x^2 + 42x + 49) -84x$$

$$= 9x^2-42x + 49$$

Using , $$(a -b)^2 = a^2 -2ab + b^2$$

$$=(3x)^2 -2(3x)(7) + (7)^2$$

$$=(3x -7)^2 =$$ RHS

Mathematics

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