Question

simplify
(12a+17b)^2 - (12a-17b)^2​

Answer 1

$\red\bigstar$Answer:

$\sf \: {( \: 12a \: + \: 17b)}^{2} \: - \: {( \: 12a \: - \: 17b)}^{2} \: = \: 816ab$

$\pink\bigstar$Given:

• $\sf \: {( \: 12a \: + \: 17b)}^{2} \: - \: {( \: 12a \: - \: 17b)}^{2}$

$\blue\bigstar$To find:

• To Simplify the given expression

$\green\bigstar$ Solution:

$\sf \: {( \: 12a \: + \: 17b)}^{2} \: - \: {( \: 12a \: - \: 17b)}^{2}$

[ By using (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b² ]

$\sf \implies {(12a)}^{2} \: + \: 2(12a)(17b) \: + \: {(17b)}^{2} \: - \: [ \: {(12a)}^{2} \: - \: 2(12a)(17b) \: + \: {(17b)}^{2}]$

$\sf \implies {(12a)}^{2} \: + \: 2(12a)(17b) \: + \: {(17b)}^{2} \: - \: {(12a)}^{2} \: + \: 2(12a)(17b) \: - \: {(17b)}^{2}$

$\sf \implies 2(12a)(17b) \: \: + \: 2(12a)(17b)$

$\sf \implies 4(12a)(17b)$

$\sf \implies \boxed{ 816ab}$

$\boxed{ \sf \therefore\sf \: {( \: 12a \: + \: 17b)}^{2} \: - \: {( \: 12a \: - \: 17b)}^{2} = \: \: 816 ab}$

$\red\bigstar$ Concepts Used:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• Negative × Negative = Positive
• Cancellation of numbers with opposite signs

$\blue\bigstar$ Extra - Information:

• a² – b² = (a + b)(a – b)

• (x + a)(x + b) = x² + (a + b) x + ab

• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

• (a + b)3 = a³ + b³ + 3ab (a + b)

• (a – b)³ = a³ – b³ – 3ab (a – b)

• a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

• If (a + b + c) = 0, then a³ + b³ + c³ = 3abc

• (a + b)² - (a - b)² = 4ab

Answer 2

Step-by-step explanation:

Here are some of my factorization rules that can help u a lot ....