Question

(a + b) give the answer by expansion​

Answer 1

(a +b)2

= (a + b)(a + b)

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

= a2 + ab + ab + b2

= a2 + 2ab + b2.

(a - b)2

= (a - b)(a - b)

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

= a2 - ab - ab + b2

= a2 - 2ab + b2.

Therefore, (a + b)2 + (a - b)2

= a2 + 2ab + b2 + a2 - 2ab + b2

= 2(a2 + b2), and

(a + b)2 - (a - b)2

= a2 + 2ab + b2 - {a2 - 2ab + b2}

= a2 + 2ab + b2 - a2 + 2ab - b2

= 4ab.

Answer 2

Answer:

Expansion of (a ± b)2

(a +b)2

= (a + b)(a + b)

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

= a2 + ab + ab + b2

= a2 + 2ab + b2.

(a - b)2

= (a - b)(a - b)

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

= a2 - ab - ab + b2

= a2 - 2ab + b2.

Therefore, (a + b)2 + (a - b)2

= a2 + 2ab + b2 + a2 - 2ab + b2

= 2(a2 + b2), and

(a + b)2 - (a - b)2

= a2 + 2ab + b2 - {a2 - 2ab + b2}

= a2 + 2ab + b2 - a2 + 2ab - b2

= 4ab.