Question

Proszę o obliczenie na podstawie wzorów skróconego mnożenia :
Wykonać działania i przeprowadzić redukcję:
a) -(3 +x)² + 5(1-x)² -3(1-x)(1+x)
b)4(m +3n)² + 3(4m-n)² - 2(m+n)(m-n)
c) -(2c +5d(2c-5d)-6(2d-5c)² +3(5c+2d)²
d)[(3x+y)²-(x+3y)²]·2xy

Answer 1

a)-(3+x)²+5(1-x)²-3(1-x)(1+x)=-(9+6x+x²)+5(1-2x+x²)-3(1-x²)=

-9-6x-x²+5-10x+5x²-3+3x²=7x²-16x-7

 

b)4(m+3n)²+3(4m-n)²-2(m+n)(m-n)=4(m²+6mn+9n²)+3(16m²-8mn+n²)-2(m²-n²)=

4m²+24mn+36n²+48m²-24mn+3n²-2m²+2n²=50m²+41n²

 

c)-(2c+5d)(2c-5d)-6(2d-5c)²+3(5c+2d)²=

-(4c²-25d²)-6(4d²-20cd+25c²)+3(25c²+20cd+4d²)=

-4c²+25d²-24d²+120cd-150c²+75c²+60cd+12d²=79c²+13d²+180cd

 

d)[(3x+y)²-(x+3y)²]·2xy=[(9x²+6xy+y²)-(x²+6xy+9y²)]·2xy=

[9x²+6xy+y²-x²-6xy-9y²]·2xy=[8x²-8y²]·2xy=16x³y-16xy³=16(x³y-xy³)