Cześć!
Szczegółowe wyjaśnienie:
Zadanie 2.
a)
[tex](p + 4)(p - 2) =p \cdot \: p - 2p + 4p - 4 \cdot2 = p {}^{2} - 2p + 4p - 8 = p {}^{2} + 2p - 8[/tex]
b)
[tex]( - 3 + a) ( a - 4) = - 3a - 3 \cdot( - 4) + a \cdot \: a - 4a = - 3a + 12 + a {}^{2} - 4a = - 7a + 12 + a {}^{2} = a {}^{2} - 7a + 12[/tex]
c)
[tex](2x + 5)(x + 3) = 2x \cdot \: x + 2x \cdot3 + 5x + 5 \cdot3 = 2x {}^{2} + 6x + 5x + 15 = \\ 2x {}^{2} + 11x + 15[/tex]
d)
[tex](4m + 1)(2 m - 5) = 4m \cdot2m - 4m \cdot5 + 2m - 5 = 8m {}^{2} - 20m + 2m - 5 = \\ 8m {}^{2} - 18m - 5[/tex]
e)
[tex](5 - p)(4 + 3p) = 5 \cdot4 + 5 \cdot3p - 4p - p \cdot3p = 20 + 15 - 4p - 3p {}^{2} = 20 + 11p - 3 p {}^{2} = \\ - 3p {}^{2} + 11p + 20[/tex]
Zadanie 3.
a)
[tex](2p + 3q)(5p + 2q) = 2p \cdot5p + 2p \cdot2q + 3q \cdot5p + 3q \cdot2q = 10p {}^{2} + 4pq + 15pq + 6q {}^{2} = \\ 10p {}^{2} + 19pq + 6q {}^{2} [/tex]
b)
[tex](3a + 2b)(a - 4b) = 3a \cdot \: a - 3a\cdot4b + 2ab - 2b \cdot4b = 3a {}^{2} - 12ab + 2ab - 8b {}^{2} = 3a {}^{2} - 10ab - 8b {}^{2} [/tex]
c)
[tex](2 - 3y)(3x - 2y) = 2x\cdot3x - 2x\cdot2y - 3y\cdot3x - 3y\cdot( - 2y) = 6x {}^{2} - 4xy - 9xy + 6y {}^{2} = 6x {}^{2} - 13xy + 6y {}^{2} [/tex]
d)
[tex](m + 2n)(5m - 2n) = m\cdot5m - 2mn + 2n \cdot5m - 2n\cdot2n = 5m {}^{2} - 2mn + 10mn - 4n {}^{2} = 5m {}^{2} + 8mn - 4n {}^{2} [/tex]
e)
[tex](5a {}^{2} - b)(2b + 3a) = 5a {}^{2} \cdot2b + 5a {}^{2} \cdot3a - b\cdot2b - 3ab = 10a {}^{2} b + 15a {}^{3} - 2b {}^{2} - 3ab[/tex]
