Question

1. (x+2y)^2 - (x+2y)(x-2y) + 2(x-2y)^2 + 4xy (tutaj ma wyjść 2x^2+16y^)

2. (5a+1)^2 + (5a-1)^2 - (5a+1)(5a-1) - 25a^2 (tutaj ma wyjść 3)

3. Zapisz w najprostszej postaci wyrażenie (3z-8)^2 - 5(3+2z)^2 + (4z+3)^2.

Oblicz jego wartość dla z=10

4. Oblicz wartość wyrażenia 2(x-3y)^2 - 3(x-2y)(x+2y) + 12xy

dla x=√6 i y=-√2

Answer 1

Wzory skróconego mnożenia:

(a+b)²=a²+2ab+b² - kwadrat sumy;

(a-b)²=a²-2ab+b² - kwadrat różnicy;

a²-b²=(a-b)(a+b) - różnica kwadratów;

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zad 1

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

=x²+4xy+4y² - (x²-4y²) + 2(x²-4xy+4y²) + 4xy=

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

=x²+16y²

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zad 2

(5a+1)^2 + (5a-1)^2 - (5a+1)(5a-1) - 25a^2=

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

=3

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zad 3

(3z-8)^2 - 5(3+2z)^2 + (4z+3)^2.=

=9z²-48z+64 - 5[9+12z+4z²] + 16z²+24z+9=

=25z²-24z+73 - 45-60z-20z²=

=5z²-84z+28=

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z=10

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=5*10²-84*10+28=

=500-840+28=

=-312

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zad 4

2(x-3y)^2 - 3(x-2y)(x+2y) + 12xy=

=2[x²-6xy+9y²]-3[x²-4y²]+12xy=

=2x²-12xy+18y²-3x²+12y²+12xy=

=-x²+30y²=

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x=√6, y=-√2

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=-(√6)²+30*(-√2)²=

=-6+30*2=

=-6+60=

=54