Question

.Verify all four identities by multiplication of binomials.

Answer 1

Given : identities (a + b)² = a² + b² + 2ab , (a - b)² = a² + b² - 2ab , (-a - b)² = a² + b² + 2ab , (a + b)(a-b) = a² - b²

To Find : Verify  by multiplication

Solution:

(a + b)² = a² + b² + 2ab

(a + b)²  = (a + b) (a + b)

using distributive property

a(a + b) + b(a + b)

= a² + ab + ba  + b²

ba = ab

= a² + ab + ab + b²

= a² + 2ab + b²

= a² + b² + 2ab

QED

(a - b)² = a² + b² - 2ab

(a - b)²  = (a - b) (a - b)

using distributive property

a(a - b) - b(a - b)

= a² - ab - ba  + (-b)(-b)  

= a² - ab - ba  + b²  

= a² - ab - ab + b²

= a² - 2ab + b²

= a² + b² - 2ab

(-a - b)² = a² + b² + 2ab

(-a - b)²  = (-a -b) (-a - b)

using distributive property

-a(-a - b) - b(-a - b)

= a² + ab + ba  + b²

= a² + 2ab + b²

= a² + b² + 2ab

QED

(a + b)(a-b) = a² - b²

(a + b)(a-b)  = a(a - b) + b(a - b)

= a² - ab + ba - b²

= a² - b²

QED

Learn more

Question 1Use a suitable identity to get each of the following ...

https://brainly.in/question/7366325

Gram panchayat of village Balipur District Mathura decided to ...

https://brainly.in/question/13328730

Answer 2

1. Given : identities (a + b)² = a² + b² + 2ab , (a - b)² = a² + b² - 2ab , (-a - b)² = a² + b² + 2ab , (a + b)(a-b) = a² - b²
2. To Find : Verify by multiplication.
3. Solution: (a + b)² = a² + b² + 2ab. (a + b)² = (a + b) (a + b) using distributive property. a(a + b) + b(a + b) = a² + ab + ba + b² ba = ab. = a² + ab + ab + b²

• , (a + b)2 = a2 + 2ab + b2
• (a – b)2 = a2 – 2ab + b2
• 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)