Question

Преобразуйте выражение в многочлен:

1. (5·a+4·b)²–(5–4·b)²;
2. (10·p–3·q)²+(5·p+6)²;
3. t·(9·t–1)²–81·t·(t–4)²;
4. 5·m·n–2·(3·m–n)²+9·m².

Спасибо)

Answer 1

1. (5·a+4·b)²–(5–4·b)²=(5а)^2+2*5а*4b+ (4b)^2-(5^2-2*5*4b+(4b)^2)=25a^2+40ab+16b^2-25+40b-16b^2=25a^2+40ab+40b-25

2. (10·p–3·q)²+(5·p+6)²=100p^2-60pq+9q^2+25p^2+60p+36=125p^2-60pq+60p+9q^2

3. t·(9·t–1)²–81·t·(t–4)²= t(81t^2-18t+1)-81t(t^2-8t+16)=81t^3-18t^2+t-81t^3+648t^2-16*81t=630t^2-1295t

4. 5·m·n–2·(3·m–n)²+9·m²= 5mn-2(9m^2-6mn+n^2)=5mn-18m^2+12mn-2n^2= -18m^2+17mn-2n^2