Question

Wykonaj działania: a) (4x-5)² + (5+4x)²

b) (2x-1)² - 4(x-3) (x+3)

c) (x+2y)² - (x+2y) (x-2y) + 2(x-2y)² + 4xy

d) (a-2b) (3a+b) - 3(a-b)²

e) (5a+1)² + (5a-1)² - (5a+1) (5a-1) - 25a²

f) (x+3y) (3y-x) - 2(x-2)² + 3 (x²-3y²)

Rozwiązanie z wykorzystaniem wzorów skróconego mnożenia. Cały zapis prosiłabym, nie same wyniki. Z góry dzięki : )

Answer 1

a) (4x-5)² + (5+4x)²=

=16x²-40x+25 + 25 +50x +16x²=

=32x²+50

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b) (2x-1)² - 4(x-3) (x+3)=

=4x²-4x+1-4x²+36=

=37-4x

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c) (x+2y)² - (x+2y) (x-2y) + 2(x-2y)² + 4xy=

=x²+4xy+4y² - x²+4y² + 2x²-8xy+8y² +4xy=

=2x²+16y²

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d) (a-2b) (3a+b) - 3(a-b)²=

=3a²-5ab-2b² - 3a²+6ab-3b²=

=ab-5b²

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e) (5a+1)² + (5a-1)² - (5a+1) (5a-1) - 25a²=

=25a²+10a+1 + 25a²-10a+1 - 25a²+1 -25a²=

=3

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f) (x+3y) (3y-x) - 2(x-2)² + 3 (x²-3y²)=

=9y²-x² - 2x²+8x-8 + 3x²-9y²=

=8x-8

Answer 2

a) (4x-5)² + (5+4x)²=16x²-40x+25+25+40x+16x²=32x²+50

 

b) (2x-1)² - 4(x-3) (x+3)=4x²-4x+1-4(x²+3x-3x-9)=4x²-4x+1-4x²+36=-4x+37

 

c) (x+2y)² - (x+2y) (x-2y) + 2(x-2y)² + 4xy=x²+4xy+4y²-(x²-2xy+2xy-4y²)+2(x²-4xy+4y²)+4xy= x²+4xy+4y²-x²+4y²+2x²-8xy+8y²+4xy=16y²+2x²

 

d) (a-2b) (3a+b) - 3(a-b)²=3a²+ab-6ab-2b²-3(a²-2ab+b²)=3a²-5ab-2b²-3a²+6ab-3b²=ab-5b²

 

e) (5a+1)² + (5a-1)² - (5a+1) (5a-1) - 25a²=25a²+10a+1+25a²-10a+1-(25a²-5a+5a-1)-25a²=50a²+2-25a²+1-25a²=3

 

f) (x+3y) (3y-x) - 2(x-2)² + 3 (x²-3y²)=3xy-x²+9y-3xy-2(x²-4x+4)+3x²-9y²=-x²+9y-2x²+8x-8+3x²-9y²=-3x²+9y+8x-8+3x²-9y=8x-8