Hi how can i simplify 3a^3b multiplied by 4(ab)^2.
Also how can i factorise x^2-4 and x^2-5x+6
Thank you
$\displaystyle 3a^3b \times 4a^2b^2$
$\displaystyle =12a^5b^3$ (Constants are multiplied and the powers are added)
$\displaystyle x^2-4$$\displaystyle =(x+2)(x-2)$
(This is difference of two squares e.g. $\displaystyle (x+a)(x-a)= x^2 - a^2$)
$\displaystyle x^2-5x+6 $
$\displaystyle =(x-2)(x-3)$
(Here you have to see what two values can be used that allow us to obtain $\displaystyle 6$ by multiplying and $\displaystyle -5$ by adding)
$\displaystyle 3a^{3b}*4{ab}^2 = 12a^{2+3b}b^2$
Tip: Review over exponents in algebra
$\displaystyle x^2-4=(x-2)(x+2)$
Tip: When you need to factor a term like this, it is usually a multiplication of conjugates.
$\displaystyle x^2-5x+6=(x-3)(x-2)$
Tip: Look at the constant term and list all the ways you can multiply two numbers to equal it. Then find the pair of numbers that add up to the coefficient in the middle.
$\displaystyle ax^2+bx+c$
You want $\displaystyle (x+D)(x+E)$ where $\displaystyle D + E = b$ and $\displaystyle D*E=c$