Question

Ch-9, algebraic expressions,ex-9.5
3.Factorise each of the following:
vi).6a⁴b² - 18a²b³
vii).2ax² + 6a²x
viii).a³-6a²
ix).6a⁴b² - 18a²b²
please answer correctly...​

Answer 1

vi).6a⁴b² - 18a²b³

= $\mathrm{Factor}\:6a^4b^2-18a^2b^3:\quad 6a^2b^2\left(a^2-3b\right)$

Steps

$6a^4b^2-18a^2b^3$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c$

$a^4b^2=a^2a^2b^2,\:a^2b^3=a^2b^2b$

$=6a^2a^2b^2-18a^2b^2b$

$\mathrm{Rewrite\:}-18\mathrm{\:as\:}3\cdot \:6$

$=6a^2a^2b^2+3\cdot \:6a^2b^2b$

$\mathrm{Factor\:out\:common\:term\:}6a^2b^2$

$=6a^2b^2\left(a^2-3b\right)$

vii).2ax² + 6a²x

= $\mathrm{Domain\:of\:}\:2ax^2+6a^2x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Axis\:interception\:points\:of}\:2ax^2+6a^2x:\quad \mathrm{X\:Intercepts}:\:\left(0,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:0\right)$

$\mathrm{X\:Intercepts}:\:\left(0,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:0\right)$

viii).a³-6a²

= $\mathrm{Factor}\:a^3-6a^2:\quad a^2\left(a-6\right)$

$a^3-6a^2$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c$

$a^3=aa^2$

$=aa^2-6a^2$

$\mathrm{Factor\:out\:common\:term\:}a^2$

$=a^2\left(a-6\right)$

ix).6a⁴b² - 18a²b²

= $\mathrm{Factor}\:6a^4b^2-18a^2b^2:\quad 6a^2b^2\left(a^2-3\right)$

$6a^4b^2-18a^2b^2$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c$

$a^4b^2=a^2a^2b^2$

$=6a^2a^2b^2-18a^2b^2$

$\mathrm{Rewrite\:}-18\mathrm{\:as\:}3\cdot \:6$

$=6a^2a^2b^2+3\cdot \:6a^2b^2$

$\mathrm{Factor\:out\:common\:term\:}6a^2b^2$

$=6a^2b^2\left(a^2-3\right)$

Hope It Helps You

Eva*

Answer 2

Answer:

Hi

Step-by-step explanation:

I have dropped some th@nks on your acc. please do the same