Question

please give me answer this my friend question
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Answer 1

Identities:

$\large \purple {\sf {1. \: {(x + y)}^{2} = {(x)}^{2} + 2xy + {(y)}^{2}}}$

$\large \purple {\sf {2. \: {(x - y)}^{2} = {(x)}^{2} - 2xy + {(y)}^{2}}}$

$\large \purple {\sf {3. \: (x + y)(x - y) = {(x)}^{2} - {(y)}^{2}}}$

Answer:

$\large \pink {\sf {{(p + 3m)}^{2} = {p}^{2} + 6pm+ {9m}^{2} }}$

$\large \pink {\sf {{(6x + 3y)}^{2} = {36x}^{2} + 36xy + {9y}^{2} }}$

$\large \pink {\sf {{(13p - 20q)}^{2} = {169p}^{2} + 520pq + {400q}^{2}}}$

$\large \pink {\sf {(6m + 3n)(6m - 3n) = {36m}^{2} - {9n}^{2}}}$

Answer 2

AnsweR :-

1] (p + 3m)²

→ (p)² + 2(p)(3m) + (3m)²

→ P² + 6pm + 9m²

2] (6x + 3y)²

→ (6x)² + 2(6x)(3y) + (3y)²

→ 36x² + 36xy + 9y²

3] (13p - 20q)²

→ (13p)² - 2(13p)(20q) + (20q)²

→ 169p² - 520pq + 400q²

4] (36x + 26y)²

→ (36x)² + 2(36x)(26y) + (26y)²

→ 1296x² + 1872xy + 676y²

5] (6m + 3 n) (6m - 3n)

→ (6m)² - (3n)²

→ 36m² - 9n²

Procedure -

$\implies$ The first question has done from the 1st identity of Algerbric identites. In this question we were given (p+3m)², now, after equating it we get p²+6pm+9m². The 1st Algerbric identity says (x+y)² = (x)² + 2xy + (y)².

$\implies$ The second equation will be solved by same identity which is has been used in the 1st equation. Then the final answer is 36x² + 36xy + 9y².

$\implies$ So, the third equation will be solved by 2nd Indentity of Algerbric identites that is (x-y)² = (x)² - 2xy + (y)². Then the final answer is 169p² - 520pq + 400q².

$\implies$ The the fourth one will solved by using the same identity as used in 2nd and 3rd equation. Then the final answer will be 1269x² + 1872xy + 676y²

$\implies$ The fifth equation will be solved by using 3rd identity of Algerbric identites that is (x+y)(x-y) = (x)² - (y)². Then the final answer will be 36m² - 9n².

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