Question

1. ((a - 6)^2)\\4. ((5p + 2)^2)\\6. ((-12 - n)^2)\\8. ((0.5x - 0.7y)^2)\polynomial that represents the area of the square.\\10. \\(\

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\le 2.)\\14. ((m + 6)(m - 6))\\16. ((2k - 4)(2k + 4))\\18. ((2.5 + 3a)(2.5 - 3a))\\20. ((7m + 8n)(7m - 8n))\\(2n)

Explanation:

Let's solve these problems one by one using the perfect square formula \((a\pm b)^2 = a^2\pm 2ab + b^2\) and the difference of squares formula \((a + b)(a - b)=a^2 - b^2\).

Problem 2: \((a - 6)^2\)

Step 1: Apply the perfect square formula \((x-y)^2=x^2-2xy + y^2\), where \(x = a\) and \(y=6\)

\((a - 6)^2=a^2-2\times a\times6+6^2\)

Step 2: Simplify the expression

\(a^2-12a + 36\)

Step 1: Apply the perfect square formula \((x + y)^2=x^2+2xy + y^2\), where \(x = 5p\) and \(y = 2\)

\((5p+2)^2=(5p)^2+2\times(5p)\times2+2^2\)

Step 2: Simplify the expression

\(25p^2 + 20p+4\)

Step 1: Rewrite \((-12 - n)^2\) as \([-(12 + n)]^2=(12 + n)^2\) (since \((-a)^2=a^2\))

Step 2: Apply the perfect square formula \((x + y)^2=x^2+2xy + y^2\), where \(x = 12\) and \(y=n\)

\((12 + n)^2=12^2+2\times12\times n+n^2\)

Step 3: Simplify the expression

\(144+24n + n^2=n^2+24n + 144\)

Answer:

\(a^2-12a + 36\)

Problem 4: \((5p + 2)^2\)