In previous chapters, we learnt how to expand and simplify various types of algebraic expressions. Now we can use these skills to manipulate more complex expressions.
Examples
Question 1
If $5x\left(x-4\right)-x\left(5x+2\right)=Ax^2+Bx$5x(x−4)−x(5x+2)=Ax2+Bx, find the values of the coefficients $A$A and $B$B.
Think: To solve this question we should concentrate first on the Left Hand Side (LHS) and expand and collect like terms. After that, we can then equate like terms between the LHS and the right.
Do:
| $\text{LHS }$LHS | $=$= | $5x\left(x-4\right)-x\left(5x+2\right)$5x(x−4)−x(5x+2) |
| $=$= | $5x^2-20x-5x^2-2x$5x2−20x−5x2−2x | |
| $=$= | $5x^2-5x^2-20x-2x$5x2−5x2−20x−2x | |
| $=$= | $-22x$−22x |
Now equate the LHS and RHS.
$-22x=Ax^2+Bx$−22x=Ax2+Bx
So because there are no $x^2$x2 terms on the LHS then $A=0$A=0 and $B=-22$B=−22
Let's have a look at some more example questions.
question 2
Simplify: $4x-4\left(7x+6x\right)$4x−4(7x+6x)
question 3
Simplify the ratio $m^2$m2$:$:$\left(m^2+m^5\right)$(m2+m5).
question 4
Expand and simplify:
$4x\left(5x^2-2x\right)-\left(4\left(3x^2-2\right)+3\right)$4x(5x2−2x)−(4(3x2−2)+3)