Answer :
To find the sum of the polynomials
[tex]$$\left(7x^3 - 4x^2\right) + \left(2x^3 - 4x^2\right),$$[/tex]
follow these steps:
1. Write the expression:
[tex]$$7x^3 - 4x^2 + 2x^3 - 4x^2.$$[/tex]
2. Combine like terms for the [tex]$x^3$[/tex] terms:
The [tex]$x^3$[/tex] terms are [tex]$7x^3$[/tex] and [tex]$2x^3$[/tex]. Adding their coefficients gives:
[tex]$$7x^3 + 2x^3 = (7 + 2)x^3 = 9x^3.$$[/tex]
3. Combine like terms for the [tex]$x^2$[/tex] terms:
The [tex]$x^2$[/tex] terms are [tex]$-4x^2$[/tex] and [tex]$-4x^2$[/tex]. Adding their coefficients gives:
[tex]$$-4x^2 - 4x^2 = (-4 -4)x^2 = -8x^2.$$[/tex]
4. Write the final simplified polynomial:
[tex]$$9x^3 - 8x^2.$$[/tex]
Thus, the sum of the polynomials is
[tex]$$\boxed{9x^3 - 8x^2}.$$[/tex]
[tex]$$\left(7x^3 - 4x^2\right) + \left(2x^3 - 4x^2\right),$$[/tex]
follow these steps:
1. Write the expression:
[tex]$$7x^3 - 4x^2 + 2x^3 - 4x^2.$$[/tex]
2. Combine like terms for the [tex]$x^3$[/tex] terms:
The [tex]$x^3$[/tex] terms are [tex]$7x^3$[/tex] and [tex]$2x^3$[/tex]. Adding their coefficients gives:
[tex]$$7x^3 + 2x^3 = (7 + 2)x^3 = 9x^3.$$[/tex]
3. Combine like terms for the [tex]$x^2$[/tex] terms:
The [tex]$x^2$[/tex] terms are [tex]$-4x^2$[/tex] and [tex]$-4x^2$[/tex]. Adding their coefficients gives:
[tex]$$-4x^2 - 4x^2 = (-4 -4)x^2 = -8x^2.$$[/tex]
4. Write the final simplified polynomial:
[tex]$$9x^3 - 8x^2.$$[/tex]
Thus, the sum of the polynomials is
[tex]$$\boxed{9x^3 - 8x^2}.$$[/tex]
