Question

expand (3-4ab) ³




with explanation please​

Answer 1

Answer:

A binomial is an algebraic expression which has exactly two terms, for example, a ± b. Its power is indicated by a superscript. For example, (a ± b)2 is a power of the binomial a ± b, the index being 2.

A trinomial is an algebraic expression which has exactly three terms, for example, a ± b ± c. Its power is also indicated by a superscript. For example, (a ± b ± c)3 is a power of the trinomial a ± b ± c, whose index is 3.

Step-by-step explanation:

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.

Corollaries:

(i) (a + b)2 - 2ab = a2 + b2

(ii) (a - b)2 + 2ab = a2 + b2

(iii) (a + b)2 - (a2 + b2) = 2ab

(iv) a2 + b2 - (a - b)2 = 2ab

(v) (a - b)2 = (a + b)2 - 4ab

(vi) (a + b)2 = (a - b)2 + 4ab

(vii) (a + 1a)2 = a2 + 2a ∙ 1a + (1a)2 = a2 + 1a2 + 2

(viii) (a - 1a)2 = a2 - 2a ∙ 1a + (1a)2 = a2 + 1a2 - 2

Thus, we have

1. (a +b)2 = a2 + 2ab + b2.

2. (a - b)2 = a2 - 2ab + b2.

3. (a + b)2 + (a - b)2 = 2(a2 + b2)

4. (a + b)2 - (a - b)2 = 4ab.

5. (a + 1a)2 = a2 + 1a2 + 2

6. (a - 1a)2 = a2 + 1a2 - 2

$hope \: it \: helps \: you$