So a times the big bracket and negative 1 times the big bracket, so if I expand it out it’s going to be a times that whole thing minus 1 times that whole thing, so a times a squared is a cubed, a times a is a squared, a times 1 is a yep and then negative 1 times a squared is negative a squared negative one times positive a is negative a and negative one times positive one is negative one now. Let’s get to the like terms, there’s a lot of a’s but we can’t gather them all together right?
We only need to gather the like terms, so a cubed there’s no other a cube, so we can’t gather them together, a squared we can look we’ve got a squared there and an a squared there and then we’ve got a and we’ve also got an a here and that’s all the like terms isn’t it?
So let’s do the gathering what’s a squared minus a squared can you guys tell me it’s zero a squared minus a squared is zero, so they cancel out and a minus a again they cancel out zero, so we’re only left with a cubed minus one that is the answer, so see how they all cancel out and it’s really nice like that but what I would do the same thing a times a big bracket, one times the big bracket like that.
So expand it out a a squared is a cubed, a times negative a negative a squared, a times 1 is a,
okay 1 times a squared is a squared now 1 times anything is it’s just itself right 1 times 2 is just 2. 1 times 100 is just 100.
So 1 times this is just as it is a squared minus a plus one, gather your like terms now we’ve got a cubed but no other a cubes we’ve got a negative a squared we’ve also got an a squared here we’ve got an a, we’ve got an a, now the good thing is they again cancel out negative a squared plus a squared they’re the same but they just have different signs so cancel out a minus a, cancel out they all cancel out so we just have a cubed plus one left that’s the answer
Algebra Algebraic Fractions Arc Binomial Expansion Capacity Common Difference Common Ratio Differentiation Double-Angle Formula Equation Exponent Exponential Function Factorials Factorise Functions Geometric Sequence Geometric Series Index Laws Inequality Integration Kinematics Length Conversion Logarithm Logarithmic Functions Mass Conversion Mathematical Induction Measurement Perfect Square Perimeter Prime Factorisation Probability Product Rule Proof Quadratic Quadratic Factorise Ratio Rational Functions Sequence Sketching Graphs Surds Time Transformation Trigonometric Functions Trigonometric Properties Volume