Simplifying Expressions

All three terms are like terms - each is a number of ys - so their coefficients can be combined. Different coefficients do not stop terms being alike.

Work left to right: $5y+3y=8y$, then $8y-2y=6y$.

The minus sign belongs to the $2y$, so that term is subtracted, not added: $5+3-2=6$.

So the expression fully simplifies to $6y$.

Use the distributive law: every term inside the bracket is multiplied by the 5 outside.

$5\times 2x=10x$ and $5\times 4=20$.

So $5(2x+4)=10x+20$. Both terms inside the bracket must be multiplied, not just the first; the 5 is multiplied by the 2, not added to it; and $2x$ and $4$ are unlike terms, so they cannot be combined before expanding.

Multiply each term inside the bracket by the 5 outside, keeping the sign with the term it belongs to.

$5\times 2x=10x$ and $5\times (-1)=-5$.

So $5(2x-1)=10x-5$.

Expand the bracket first: $3\times x=3x$ and $3\times (-2)=-6$, so $3(x-2)=3x-6$.

The expression becomes $4x+3x-6$.

Now collect the like terms: $4x+3x=7x$. The $-6$ has no like term, so it stays as it is and cannot be merged into the $x$ term.

The simplified expression is $7x-6$.

Expand the bracket first: $2\times 4x=8x$ and $2\times 5=10$, so $2(4x+5)=8x+10$.

The expression becomes $8x+10-3x$.

Only $8x$ and $-3x$ are like terms: $8x-3x=5x$. The 10 is a number on its own, so the $3x$ cannot be taken away from it.

The simplified expression is $5x+10$.

Expand each bracket, taking the sign in front of the bracket with it.

$2(x+3)=2x+6$.

For the second bracket the multiplier is $-5$: $-5\times 2x=-10x$ and $-5\times (-1)=+5$, so $-5(2x-1)=-10x+5$.

Now collect like terms: $2x-10x=-8x$ and $6+5=11$.

The simplified expression is $-8x+11$.