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
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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
=======================
zad 2
(5a+1)^2 + (5a-1)^2 - (5a+1)(5a-1) - 25a^2=
=25a²+10a+1 + 25a²-10a+1 - 25a²+1 -25a²=
=3
=======================
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=
---
z=10
---
=5*10²-84*10+28=
=500-840+28=
=-312
=======================
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=
---
x=√6, y=-√2
---
=-(√6)²+30*(-√2)²=
=-6+30*2=
=-6+60=
=54