You have seen that expressions consist of terms and last week we looked at the distributive law that allows us to expand and simplify terms such as: 2(3x +4) into 2(3x) + 2(4) = 6x +8.
Here are three short problems for you to warm up with:
a) 3(11x² – 2) b) 4a(2a – 3b) c) 6a(2ax + 4b)
Compare your answers with each others.
Now on to today’s work: We can add or subtract expressions and polynomials by combining the like terms (hamburgers with hamburgers, chips with chips remember?) So
2x² + 4x + 6 can be added to 3x² + 2x +3 to give us (2x² + 3x²) + (4x + 2x) + (6 +3) = 5x² + 6x + 9
Here is another example (-4a² + a – 6 ) + (2a² – a + 5) = -2a² (note the sign) -1 (there is no a because they cancel each other out)
Try this one on your own: 4b² -5b added to -3b² + 6b – 4
It is also possible to subtract polynomials in the same fashion:
Subtract 3b² + 4b -5 from 5b² + 6b + 1 (Tip write the two expressions one under the other)
5b² + 6b + 1
– (3b² + 4b -5) (Now change the signs because you are subtracting so
5b² + 6b + 1
–3b² – 4b +5 (Now add)
= 2b² + 2b + 6
Now do these ones on your own for practice:
(d) 4ab² + 2ab + 7 added to -3ab² – 3ab +1
(e)( 6xy -9 ) + (4x²y + 2 xy – 2)
(f) (2a²b – 3ab + b) + (-2a² – 2a²b + 4ab +3)
(g) Subtract 4ab² + 2ab + 7 from -3ab² – 3ab +1
(h) (4x²y + 2 xy – 2) – ( 6xy -9 )
What’s coming next? In the next lesson we will look at how to multiply binomials
Here is a teaser for you to see if you can work out how to do it:
(6a -3)(4a + 2) = ?