Question

(12x + 5y )² - (12y-5x )² = ?​

Answer 1

Answer:

We know that (a+b)²=a²+2ab+b²

(a-b)²=a²-2ab+b²

So, [(12x)²+2(12x)(5y)+(5y)²]-[(12y)²-2(12y)(5x)+(5x)²]

(144x²+120xy+25y²)-(144y²-120xy+25x²)

144x²+120xy+25y²-144y²+120xy-25x²

144x²-25x²+120xy+120xy+25y²-144y²

119x²+240xy-119y²

119x²-119y²+240xy

You can solve it more by equation (a²-b²)=(a+b)(a-b)

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Answer 2

Answer:

${(12x + 5y)}^{2} - {(12y - 5x)}^{2} \\ = {(12x)}^{2} + {(5y)}^{2} + 2(12x)(5y) - ( {(12y)}^{2} + {(5x)}^{2} - 2(12y)(5x)) \\ = 144 {x}^{2} + 25 {y}^{2} + 120xy - ( 144 {y}^{2} + 25 {x}^{2} - 120xy) \\ = 144 {x}^{2} + 25 {y}^{2} + 120xy - 144 {y}^{2} - 25 {x}^{2} + 120xy \\ = (144x^2+(−25x^2))+(120xy+120xy)+(25y^2+(−144y^2))\\\: \: \large{\underline{\underline{ 119x^2+240xy-119y^2}}}$