Question

Представьте в виде многочлена выражение 1) (p+8)^2. 2) (10x-3y)^2 3) (x-9)(x+9) 4) (4m+7n)(7n-4m)

Answer 1

$1)~ (p+8)^2=p^2+16p+64\\ 2)~ (10x-3y)^2=100x^2-60xy+9y^2\\ 3)~ (x-9)(x+9)=x^2-81\\ 4)~ (4m+7n)(7n-4m)=(7n+4m)(7n-4m)=49n^2-16m^2$

Answer 2

1. (p + 8)^2:

(p + 8)^2 = p^2 + 2p*8 + 8^2 = p^2 + 16p + 64

2. (10x - 3y)^2:

(10x - 3y)^2 = (10x)^2 + 2*(10x)*(-3y) + (-3y)^2 = 100x^2 - 60xy + 9y^2

3. (x - 9)(x + 9):

(x - 9)(x + 9) = x^2 - 9^2 = x^2 - 81

4. (4m + 7n)(7n - 4m):

(4m + 7n)(7n - 4m) = (4m)(7n) + (4m)(-4m) + (7n)(7n) + (7n)(-4m) = 28mn - 16m^2 + 49n^2 - 28mn = -16m^2 + 49n^2