Recall that multiplication and addition are commutative, i.e.

a + b = b + a
a x b = b x a,

associative, i.e.

a + (b + c) = (a + b) + c
a x (b x c) = (a x b) x c

and distributive, i.e.

a x (b + c) = a x b + a x c

We will use the commutative and distributive rules to look at some of these.

Rewriting 152 as 153 - 1,

169 x 152
= 169 x (153 - 1)
= 169 x 153 - 169 x 1 (distributive rule)
= 153 x 169 - 169 x 1 (commutative rule)
= L - 169

Rewriting 168 as 169 - 1,

153 x 168
= 153 x (169 - 1)
= 153 x 169 - 153 x 1 (distributive rule)
= L - 153
= L + (-153) (we can view subtraction as the addition of a negative number)

Rewriting 154 as 153 + 1,

154 x 169
= (153 + 1) x 169
= 153 x 169 + 1 x 169 (distributive rule)
= L + 169

Rewriting 170 as 169 + 1,

153 x 170
= 153 x (169 + 1)
= 153 x 169 + 153 x 1 (distributive rule)
= L + 153

Therefore,

169 x 152 + 153 x 168 - [(-154) x 169 + (-153 x 170)]
= 169 x 152 + 153 x 168 + 154 x 169 + 153 x 170 (yes, distributive rule applies even with the negative sign there; here, the negative sign is distributed to the two negative signs to make them positive because negative times negative is positive)
= (L - 169) + (L - 153) + (L + 169) + (L + 153)
= L - 169 + L - 153 + L + 169 + L + 153
= L + L + L + L + 169 - 169 + 153 - 153 (commutative rule applies)
= L + L + L + L
= 4 x L
= 4 x (153 x 169)
= 4 x 25 857
= 103 428