Question

Place the indicated product in the proper location on the grid. (4x^3+7y^3 z^ 4) ^2

Answer 1

`16x^(6) +56x^(3)y^(3) z^(4) +49y^(6) z^(8) \\`

Explanation:

To solve this type of problems first need to review some laws of exponents:

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

`x^(2) +x^(8)  = x^(2+8)  = x^(10)`

When you are raising a base with power to another power, you should keep the base and multiply the exponents:

`(x^(2) y^(5))^3 = x^(2*3) y^(5*3) = x^(6) y^(15)`

Now for the expression
`(4x^(3) + 7y^(3) z^(4) )^2`

Write the multiplying factors:

`(4x^(3) + 7y^(3) z^(4) )(4x^(3) + 7y^(3) z^(4) )`

Multiply the term
`4x^(3)`

`(4x^(3) + 7y^(3) z^(4) )(4x^(3) + 7y^(3) z^(4) ) = 16x^(3+3) + 28x^3y^(3) z^(4)`

Then multiply the term
`<strong>7y^(3)z^(4)</strong>`

`(4x^(3) + 7y^(3) z^(4) )(4x^(3) + 7y^(3) z^(4) ) = 16x^(3+3) + 28x^3y^(3) z^(4)\\\\<strong>+ 28x^3y^(3) z^(4) + 49y^(3+3) z^(4+4)</strong>`

Simplify the exponents:

`(4x^(3) + 7y^(3) z^(4) )(4x^(3) + 7y^(3) z^(4) ) = 16x^(6) + 28x^3y^(3) z^(4)\\\\+ 28x^3y^(3) z^(4) + 49y^(6) z^(8)`

Add like terms:

`= 16x^(6) + 56x^3y^(3) z^(4) + 49y^(6) z^(8)`