Zadanie 1.16-1.
Zapisz w postaci sumy algebraicznej.
a) $(x+5)^2=$
?
\(x^{2}+10x+25\)
b) $(x-4)^2=$
?
\(x^{2}-8x+16\)
c) $(3x+2)^2=$
?
\(9x^{2}+12x+4\)
d) $(2x-5)^2=$
?
\(4x^{2}-20x+25\)
e) $(x+1)^2=$
?
\(x^{2}+2x+1\)
f) $(x+2)^2=$
?
\(x^{2}+4x+4\)
g) $(x-3)^2=$
?
\(x^{2}-6x+9\)
h) $(x-5)^2=$
?
\(x^{2}-10x+25\)
i) $(2x+1)^2=$
?
\(4x^{2}+4x+1\)
j) $(4x-1)^2=$
?
\(16x^{2}-8x+1\)
k) $(7-x)^2=$
?
\(x^{2}-14x+49\)
l) $(2x+4)^2=$
?
\(4x^{2}+16x+16\)
m) $(3x+8)^2=$
?
\(9x^{2}+48x+64\)
n) $\left(x+\frac12\right)^2=$
?
\(x^{2}+x+\frac{1}{4}\)
o) $\left(2x-\frac12\right)^2=$
?
\(4x^{2}-2x+\frac{1}{4}\)
p) $\left(\frac12 x+2\right)^2=$
?
\(\frac{1}{4}x^{2}+2x+4\)
q) $\left(\frac{x}{2}+8\right)^2=$
?
\(\frac{1}{4}x^{2}+8x+64\)
r) $\left(\frac32 x-6\right)^2=$
?
\(\frac{9}{4}x^{2}-18x+36\)
s) $(0{,}5x+0{,}4)^2=$
?
\(0{,}25x^{2}+0{,}4x+0{,}16\)
t) $(0{,}1x-2{,}5)^2=$
?
\(0{,}01x^{2}-0{,}5x+6{,}25\)
Zadanie 1.16-2.
Zapisz w postaci sumy algebraicznej.
a) $(x+4y)^2=$
?
\(x^{2}+8xy+16y^{2}\)
b) $(2x-3y)^2=$
?
\(4x^{2}-12xy+9y^{2}\)
c) $(x+2y)^2=$
?
\(x^{2}+4xy+4y^{2}\)
d) $(2x-y)^2=$
?
\(4x^{2}-4xy+y^{2}\)
e) $(3x+2y)^2=$
?
\(9x^{2}+12xy+4y^{2}\)
f) $(3x-4y)^2=$
?
\(9x^{2}-24xy+16y^{2}\)
g) $\left(x-\frac12 y\right)^2=$
?
\(x^{2}-xy+\frac{1}{4}y^{2}\)
h) $\left(3x+\frac12 y\right)^2=$
?
\(9x^{2}+3xy+\frac{1}{4}y^{2}\)
i) $\left(2x-\frac12 y\right)^2=$
?
\(4x^{2}-2xy+\frac{1}{4}y^{2}\)
j) $\left(\frac12 x+\frac13 y\right)^2=$
?
\(\frac{1}{4}x^{2}+\frac{1}{3}xy+\frac{1}{9}y^{2}\)
Zadanie 1.16-3.
Oblicz.
a) $(\sqrt5+2)^2=$
?
\(9+4\sqrt{5}\)
b) $(\sqrt6+\sqrt2)^2=$
?
\(8+4\sqrt{3}\)
c) $(\sqrt6-\sqrt3)^2=$
?
\(9-6\sqrt{2}\)
d) $(\sqrt7+1)^2=$
?
\(8+2\sqrt{7}\)
e) $(\sqrt5-3)^2=$
?
\(14-6\sqrt{5}\)
f) $(6-\sqrt3)^2=$
?
\(39-12\sqrt{3}\)
g) $(4+\sqrt5)^2=$
?
\(21+8\sqrt{5}\)
h) $(\sqrt3+\sqrt2)^2=$
?
\(5+2\sqrt{6}\)
i) $(\sqrt7-\sqrt5)^2=$
?
\(12-2\sqrt{35}\)
j) $(\sqrt6+\sqrt{15})^2=$
?
\(21+6\sqrt{10}\)
k) $(3+\sqrt2)^2=$
?
\(11+6\sqrt{2}\)
l) $(1-\sqrt5)^2=$
?
\(6-2\sqrt{5}\)
m) $(4-3\sqrt2)^2=$
?
\(34-24\sqrt{2}\)
n) $(2\sqrt7+3)^2=$
?
\(37+12\sqrt{7}\)
o) $(2\sqrt5+\sqrt3)^2=$
?
\(23+4\sqrt{15}\)
p) $(\sqrt6-2\sqrt3)^2=$
?
\(18-12\sqrt{2}\)
q) $\left(\frac{\sqrt2}{2}-\sqrt6\right)^2=$
?
\(\frac{13}{2}-2\sqrt{3}\)
r) $\left(8-\frac{\sqrt2}{2}\right)^2=$
?
\(\frac{129}{2}-8\sqrt{2}\)
s) $\left(\frac{\sqrt2}{2}+\sqrt3\right)^2=$
?
\(\frac{7}{2}+\sqrt{6}\)