Aby pomnożyć dwie sumy algebraiczne, mnożymy każdy składnik pierwszej sumy przez każdy składnik drugiej sumy: $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$ $\left(a-b\right)\left(c+d\right)=a\cdot c+a\cdot d-b\cdot c-b\cdot d$  $\left(a+b\right)\left(c-d\right)=a\cdot c-a\cdot d+b\cdot c-b\cdot d$  $\left(a-b\right)\left(c-d\right)=a\cdot c-a\cdot d-b\cdot c+b\cdot d$

---

a)

$\left(x+4\right)\left(x-3\right)=x\cdot x-x\cdot 3+4\cdot x-4\cdot 3=$

$=x^2-3x+4x-12=x^2+x-12$

---

b)

$\left(5a-b\right)\left(5a+b\right)=5a\cdot 5a+5a\cdot b-b\cdot 5a-b\cdot b=$

$=25a^2+5ab-5ab-b^2=25a^2-b^2$

---

c)

$\left(2x+3y\right)\left(6xy-3x\right)=2x\cdot 6xy-2x\cdot 3x+3y\cdot 6xy-3y\cdot 3x=$

$=12x^{2}y-6x^2+18x{y}^2-9xy$

---

d)

$\left(4x^3-2y\right)\left(3x-4y^2\right)=4x^3\cdot 3x-4x^3\cdot 4y^2-2y\cdot 3x+2y\cdot 4y^2=$

$=12x^4-16x^3{y}^2-6xy+8y^3$

---

e)

${\left(m+5\right)}^2=\left(m+5\right)\left(m+5\right)=m\cdot m+m\cdot 5+5\cdot m+5\cdot 5=$

$=m^2+5m+5m+25=m^2+10m+25$

---

f)

${\left(6+5x\right)}^2=\left(6+5x\right)\left(6+5x\right)=6\cdot 6+6\cdot 5x+5x\cdot 6+5x\cdot 5x=$

$=36+30x+30x+25x^2=36+60x+25x^2$

---

g)

${\left(3-n\right)}^2=\left(3-n\right)\left(3-n\right)=3\cdot 3-3\cdot n-n\cdot 3+n\cdot n=$

$=9-3n-3n+n^2=9-6n+n^2$

---

h)

${\left(4a-5\right)}^2=\left(4a-5\right)\left(4a-5\right)=4a\cdot 4a-4a\cdot 5-5\cdot 4a+5\cdot 5=$

$=16a^2-20a-20a+25=16a^2-40a+25$