# Math Help - Some basic algebra equations

1. ## Some basic algebra equations

Again, to fly through the afternoon, I've given the team some more maths to keep their brains bubbling!

Could someone please provide for the answers and working for the following:

2. A)
\begin{aligned}
x(x + 4) &= 21 \\
x^2 + 4x &= 21 \\
x^2 + 4x - 21 &= 0 \\
(x + 7)(x - 3) &= 0 \\
x + 7 &= 0\;\;\Rightarrow\;\; x = -7 \\
x - 3 &= 0\;\;\Rightarrow\;\; x = 3
\end{aligned}

B)
\begin{aligned}
\frac{x - 1}{3} - \frac{x - 1}{2} &= 6 \\
6\left(\frac{x - 1}{3} - \frac{x - 1}{2}\right) &= 6(6) \\
2(x - 1) - 3(x - 1) &= 36 \\
2x - 2 - 3x + 3 &= 36 \\
-x + 1 &= 36 \\
-x &= 35 \\
x &= -35
\end{aligned}

01

Could someone please attempt the first section

4. $(3x^2)^4=3^4x^8$

5. $(a)\;9xy+8y-4y^2 +9y-2x^2y=9xy+17y-4y^2 -2x^2 y$

$(b)\;(3x^2)^4=3^4\times (x^2)^4=81x^8$

$(c)\;\frac{24x^6 y^2}{6x^2 y}=\frac{4x^6y^2}{x^2 y}=4x^4 y$

$(d)\;\frac{8x-6(2x+4)+10)}{8}=\frac{8x-12x-24+10}{8}$ $\;=\frac{-4x-14}{8}=\frac{-2(2x+7)}{8}=-\frac{2x+7}{4}$

6. Thank you very much again!