Question

OBLICZ:

a) (x-2)^{2} + (2x-3)^{2}

b) (3y-1)^{2} - (2y-5) (2y+5) -3y^{2}

c) (5a-2) (5a+2) - (3a-1)^{2} +4a^{2}

d) (4b+3)^{2} - 2(b-3) ^{2}(b+3) - (b-1)^{2}

Answer 1

a) (x-2)²+(2x-3)²=x²-4x+4+4x²-12x+9=5x²-16x+13

b) (3y-1)²-(2y-5)(2y+5)-3y²=9y²-6y+1-(4y²-25)-3y²=9y²-6y+1-4y²+25-3y²=2y²-6y+26

c) (5a-2)(5a+2)-(3a-1)²+4a²=25a²-4-9a²+6a-1+4a²= 20a²-5+6a

d) (4b+3)²-2(b-3)²(b+3)-(b-1)²=16b²+24b+9-2(b²-6b+9)(b+3)-b²+2b-1=16b²+24b+9-2b³+6b²+18b-54-b²+2b-1=21b²+44b-2b³-45

Answer 2

a)(x-2)²+(2x-3)²=x²-4x+4+4x²-12x+9=5x²-16x+13

b) (3y-1)² - (2y-5) (2y+5) -3y²=9y²-6y+1-(4y²-25)-3y²=9y²-6y+1-4y²+25-3y²=2y²-6y+26

c) (5a-2) (5a+2) - (3a-1)² +4a²=25a²-4-(9a²-6a+1)+4a²=25a²-4-9a²+6a-1+4a²=20a²+6a-5

d) (4b+3)² - 2(b-3)²(b+3) - (b-1)²=16b²+24b+9-2(b²-6b+9)(b+3)-(b²-2b+1)=16b²+24b+9-2(b³-6b²+9b+3b²-18b+27)-b²+2b-1=16b²+24b+9-2b³+12b²-18b-6b²+36b-54-b²+2b-1=-2b³+21b²+44b+8