how would you factor xy+4y+xz+4z
thanks in advance
x(y + z) + 4 (y + z) = (x+4)(y+z)
To factor the expression xy+4y+xz+4z, we can use the distributive property and group the common terms together.
Step 1: Group the terms with common factors.
xy + 4y + xz + 4z = (xy + 4y) + (xz + 4z)
Step 2: Factor out the common factor from each group.
xy + 4y = y(x + 4)
xz + 4z = z(x + 4)
Step 3: Notice that both groups have a common factor of (x + 4).
Step 4: Write the factored form by factoring out the common factor.
(xy + 4y) + (xz + 4z) = y(x + 4) + z(x + 4)
Step 5: Factor out the common factor again to simplify the expression.
y(x + 4) + z(x + 4) = (x + 4) * (y + z)
Therefore, the factored form of xy + 4y + xz + 4z is (x + 4)(y + z).