Simplifying Polynomials - Distributive Property and Combining Like Terms
Distributive property of multiplication - states that when a number is multiplied by the sum
of two numbers, the first number can be distributed to both of those numbers and
multiplied by each of them separately, then adding the two products together for the
same result as multiplying the first number by the sum.
We can simplify polynomials using the distributive property of multiplication. e. g.
a( x - y ) = ax - ay , variable a is distributed to both terms x - y.
3x(5a + 2b + cx) = 15ax + 6bx + 3cx2 , is another example.
In case terms have the same variables, the product rule of exponent is applied.
𝑥 𝑎 𝑥 𝑏 = 𝑥 𝑎+𝑏
Exercises:
1. 4xy2(2a2 + 3b2 - xy)
2. 4z2(ab - 4xy + 2yz2 + 2b3)
3. -m(2am - 3nm2 - nmx)
4. 2xy3(-3ab + 2ab3 - 4xy)
5. 5ay4(2yz2 + 3b2 + 3nm2 - 2ab3 + nmx)
6. -ax(axy + x2y - ay2)
7. bm(-abm + aby)
8. 3x(2xy - 4xz + 3xz3)
Distributive property of multiplication - states that when a number is multiplied by the sum
of two numbers, the first number can be distributed to both of those numbers and
multiplied by each of them separately, then adding the two products together for the
same result as multiplying the first number by the sum.
We can simplify polynomials using the distributive property of multiplication. e. g.
a( x - y ) = ax - ay , variable a is distributed to both terms x - y.
3x(5a + 2b + cx) = 15ax + 6bx + 3cx2 , is another example.
In case terms have the same variables, the product rule of exponent is applied.
𝑥 𝑎 𝑥 𝑏 = 𝑥 𝑎+𝑏
Exercises:
1. 4xy2(2a2 + 3b2 - xy)
2. 4z2(ab - 4xy + 2yz2 + 2b3)
3. -m(2am - 3nm2 - nmx)
4. 2xy3(-3ab + 2ab3 - 4xy)
5. 5ay4(2yz2 + 3b2 + 3nm2 - 2ab3 + nmx)
6. -ax(axy + x2y - ay2)
7. bm(-abm + aby)
8. 3x(2xy - 4xz + 3xz3)
