Multiplying 2 term × 3 terms

####
(a + 7) × (a
^{
2
}
+ 3a + 5)

= a × (a
^{
2
}
+3a+5) + 7 × (a
^{
2
}
+ 3a + 5)

= a × a
^{
2
}
+ a × 3a + a × 5 + 7 × a
^{
2
}
+ 7 × 3a + 7 × 5

= a
^{
3
}
+ 3a
^{
2
}
+ 5a + 7a
^{
2
}
+ 21a + 35

= a
^{
3
}
+ (3a
^{
2
}
+ 7a
^{
2
}
) + (5a + 21a) + 35

= a
^{
3
}
+ 10a
^{
2
}
+ 26a + 35

####
(x + 2) × (x
^{
2
}
+ 4x + 4)

= 𝑥 × (x
^{
2
}
+ 4x + 4) + 2 × (x
^{
2
}
+ 4𝑥 + 4)

= 𝑥 × x
^{
2
}
+ 𝑥 × 4𝑥 + 𝑥 × 4 + 2 × x
^{
2
}
+ 2 × 4𝑥 + 2 × 4

= x
^{
3
}
+ 4x
^{
2
}
+ 4x + 2x
^{
2
}
+ 8x + 8

= x
^{
3
}
+ 4x
^{
2
}
+ 2x
^{
2
}
+ 4x + 8x + 8

= x
^{
3
}
+ 6x
^{
2
}
+ 12x + 8