Poproszę tylko o zadanie 4 (wzory skróconego mnożenia)
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.
===============================
a) (2x+4)²=
=(2x)²+2*2x*4+4²=
=4x²+16x+16
--------------------------------------------------------------
b) (3+2x)²=
=3²+2*3*2x+(2x)²=
=9+12x+4x²
c) (4y²+1)²=
=(4y²)²+2*4y²*1+1²=
=16y⁴+8y²+1
d) (2x-3)²=
=(2x)²-2*2x*3+3²=
=4x²-12x+9
e) (4-2m)²=
=4²-2*4*2m+(2m)²=
=16-16m+4m²
f) (ax-5a)²=
=(ax)²-2*ax*5a+(5a)²=
=a²x²-10a²x+25a²
g) (2-√3)²=
=2²-2*2*√3+√3²=
=4-4√3+3=
=7-4√3
h) (1+√2)²=
=1²+2*1*√2+√2²=
=1+2√2+2=
=3+2√2
i) (2y+3z)(2y-3z)=
=(2y)²-(3z)²=
=4y²-9z²
j) (2xy-3mn)(2xy+3mn)=
=(2xy)²-(3mn)²=
=4x²y²-9m²n²
k) (√5-2)(√5+2)=
=√5²-2²=
=5-4=
=1
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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.
===============================
a) (2x+4)²=
=(2x)²+2*2x*4+4²=
=4x²+16x+16
--------------------------------------------------------------
b) (3+2x)²=
=3²+2*3*2x+(2x)²=
=9+12x+4x²
--------------------------------------------------------------
c) (4y²+1)²=
=(4y²)²+2*4y²*1+1²=
=16y⁴+8y²+1
--------------------------------------------------------------
d) (2x-3)²=
=(2x)²-2*2x*3+3²=
=4x²-12x+9
--------------------------------------------------------------
e) (4-2m)²=
=4²-2*4*2m+(2m)²=
=16-16m+4m²
--------------------------------------------------------------
f) (ax-5a)²=
=(ax)²-2*ax*5a+(5a)²=
=a²x²-10a²x+25a²
--------------------------------------------------------------
g) (2-√3)²=
=2²-2*2*√3+√3²=
=4-4√3+3=
=7-4√3
--------------------------------------------------------------
h) (1+√2)²=
=1²+2*1*√2+√2²=
=1+2√2+2=
=3+2√2
--------------------------------------------------------------
i) (2y+3z)(2y-3z)=
=(2y)²-(3z)²=
=4y²-9z²
--------------------------------------------------------------
j) (2xy-3mn)(2xy+3mn)=
=(2xy)²-(3mn)²=
=4x²y²-9m²n²
--------------------------------------------------------------
k) (√5-2)(√5+2)=
=√5²-2²=
=5-4=
=1