We will discuss here about the Simplification of (a + b)(a – b).
(a + b)(a – b) = a(a – b) + b(a – b)
= a\(^{2}\) - ab + ba - b\(^{2}\)
= a\(^{2}\) - b\(^{2}\)
Thus, we have (a + b)(a - b) = a\(^{2}\) - b\(^{2}\)
Solved Examples on Simplification of (a + b)(a – b)
1. Simplify: (3m – 4n + 2)(3m – 4n – 2)
Solution:
Given expression = (3m – 4n + 2)(3m – 4n – 2)
= [(3m – 4n) + 2][(3m – 4n) – 2]
Let 3m – 4n = x. Then,
Given expression = (x + 2)(x – 2)
= x\(^{2}\) – 2\(^{2}\)
= x\(^{2}\) – 4
= (3m – 4n)\(^{2}\) – 4, [plug-in x = 3m – 4n]
= (3m)\(^{2}\) – 2 ∙ 3m ∙ 4n + (4n)\(^{2}\) - 4
= 9m\(^{2}\) – 24mn + 16n\(^{2}\) – 4.
2. Simplify: (z - \(\frac{1}{z}\) + 3)(z + \(\frac{1}{z}\) + 3)
Solution:
Given expression = (z - \(\frac{1}{z}\) + 3)(z + \(\frac{1}{z}\) + 3)
= [(z + 3) - \(\frac{1}{z}\)][(z + 3) + \(\frac{1}{z}\)]
Let z + 3 = k. Then,
Given expression = (k - \(\frac{1}{z}\))(k + \(\frac{1}{z}\))
= k\(^{2}\) – (\(\frac{1}{z}\))\(^{2}\)
= (z + 3)\(^{2}\) – (\(\frac{1}{z}\))\(^{2}\), [plug-in k = z + 3]
= z\(^{2}\) + 2 ∙ z ∙ 3 + 3\(^{2}\) - \(\frac{1}{z^{2}}\)
= z\(^{2}\) + 6z + 9 - \(\frac{1}{z^{2}}\).
From Simplification of (a + b)(a – b) to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Oct 08, 24 10:53 AM
Oct 07, 24 04:07 PM
Oct 07, 24 03:29 PM
Oct 07, 24 03:13 PM
Oct 07, 24 12:01 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.