Question

Place the indicated product in the proper location on the grid. (3x ^2a - 4y ^a z^3a)^ 2

Answer 1

Answer:

$9x^{4a} -24x^{2a}y^{a}  z^{3a}  + 16y^{2a} z^{6a}$

Step-by-step explanation:

You can follow this steps:

For the expression:

$(3x^{2a} - 4y^{2} z^{3a} )^{2}$

Write the factors:

$(3x^{2a} - 4y^{2} z^{3a} )(3x^{2a} - 4y^{2} z^{3a} )$

Now multiply by the term $3x^{2a}$

$(3x^{2a} - 4y^{2} z^{3a} )(3x^{2a} - 4y^{2} z^{3a} ) = 9x^{4a} -12x^{2a} y^{a} z^{3a}$

Then multiply by the term $-4y^{2}$

$(3x^{2a} - 4y^{2} z^{3a} )(3x^{2a} - 4y^{2} z^{3a} ) = 9x^{4a} -12x^{2a} y^{a} z^{3a} \\\\             -12x^{2a} y^{a} z^{3a} + 16y^{2a} z^{6a}$

Finally add the terms:

$= 9x^{4a} -24x^{2a} y^{a} z^{3a} + 16y^{2a} z^{6a}$

You will need to review the laws for the exponents.

For example:

When you are multiplying with the same base you need to add the exponents.

$x^{2} *x^{5} = x^{2+5} = x^{7}$

Power to power, you multiply the exponents but keep the same base:

$(x^{2}y)^3 = (x^{2*3} y^3) = x^{6} y^3$