Multiplying 1 term with 2 terms and 1 term with 3 terms or more

#### 3x × (5y + 2)

= 3x × 5y + 3x × 2

= 15xy + 6x

#### (−5y + 2) × (−3x)

= (−5y) × (−3x) + 2 × (−3x)

= 5y × 3x – 2 × 3x

= 15xy − 6x

#### 2x × (3x + 5xy)

= 2x × 3x + 2x × 5xy

= 2 × 3 × x × x + 2 × 5 × x × x × y

= 6x
^{
2
}
+ 10x
^{
2
}
y

####
5xy × (y
^{
2
}
+ 3)

= 5xy × y
^{
2
}
+ 5xy × 3

= 5 × x × y × y
^{
2
}
+ 5 × 3 × x × y

= 5 xy
^{
3
}
+ 15xy

####
a
^{
2
}
(2ab − 5c)

= a
^{
2
}
× 2ab − a
^{
2
}
× 5c

= 2 × a
^{
2
}
× a × b − 5 × a
^{
2
}
× c

= 2a
^{
3
}
b − 5a
^{
2
}
c

####
3p × (4p
^{
2
}
+ 5p + 7)

= 3p × 4p
^{
2
}
+ 3𝑝 × 5𝑝 + 3𝑝 × 7

= 3 × 4 × 𝑝 × p
^{
2
}
+ 3 × 5 × 𝑝 × p + 3 × 7 × 𝑝

= 12p
^{
3
}
+ 15p
^{
2
}
+ 21𝑝

####
(4p
^{
2
}
+ 5p + 7) × 3p

= 4p
^{
2
}
× 3𝑝 + 5𝑝 × 3𝑝 + 7 × 3𝑝

= 12p
^{
3
}
+ 15p
^{
2
}
+ 21𝑝