問題
次の多項式 $A, B$ について, $A+B$ と $A-B$ を計算せよ.
解説
- (1) $A = 7x – 5y + 17,\quad B = 6x + 13y – 5$
- $A+B$
$=7x-5y+17+(6x+13y-5)$
$=$$13x+8y+12$ - $A-B$
$=7x-5y+17-(6x+13y-5)$
$=$$x-18y+22$
- $A+B$
- (2) $A = -3x^2 – 2x – 1,\quad B = 2x^2 + 7x + 3$
- $A+B$
$=-3x^2 – 2x – 1+(2x^2 + 7x + 3)$
$=$$-x^2+5x+2$ - $A-B$
$=-3x^2 – 2x – 1-(2x^2 + 7x + 3)$
$=$$-5x^2-9x-4$
- $A+B$
- (3) $A = 5x^2 – 2xy + y^2,\quad B = -3x^2 + 3xy – 4y^2$
- $A+B$
$=5x^2 – 2xy + y^2+(-3x^2 + 3xy – 4y^2)$
$=$$2x^2+xy-3y^2$ - $A-B$
$=5x^2 – 2xy + y^2-(-3x^2 + 3xy – 4y^2)$
$=$$8x^2-5xy+5y^2$
- $A+B$
- (4) $A = x^3 – 3 + 2x^2,\quad B = -5x + 2x^2 – x^3 – 1$
- $A+B$\\
$=x^3 – 3 + 2x^2+(-5x + 2x^2 – x^3 – 1)$
$=$$4x^2-5x-4$ - $A-B$
$=x^3 – 3 + 2x^2-(-5x + 2x^2 – x^3 – 1)$
$=$$2x^3+5x-2$
- $A+B$\\