Answer :
To multiply the expression
[tex]$$5x^2 \left(2x^2 + 13x - 5\right),$$[/tex]
we need to distribute [tex]$5x^2$[/tex] to each term inside the parentheses:
1. Multiply [tex]$5x^2$[/tex] by [tex]$2x^2$[/tex]:
[tex]$$5x^2 \cdot 2x^2 = (5 \cdot 2)(x^2 \cdot x^2) = 10x^4.$$[/tex]
2. Multiply [tex]$5x^2$[/tex] by [tex]$13x$[/tex]:
[tex]$$5x^2 \cdot 13x = (5 \cdot 13)(x^2 \cdot x) = 65x^3.$$[/tex]
3. Multiply [tex]$5x^2$[/tex] by [tex]$-5$[/tex]:
[tex]$$5x^2 \cdot (-5) = 5 \cdot (-5)x^2 = -25x^2.$$[/tex]
Now, combine all the terms to get the final expanded expression:
[tex]$$10x^4 + 65x^3 - 25x^2.$$[/tex]
Thus, the answer is
[tex]$$\boxed{10x^4 + 65x^3 - 25x^2}.$$[/tex]
[tex]$$5x^2 \left(2x^2 + 13x - 5\right),$$[/tex]
we need to distribute [tex]$5x^2$[/tex] to each term inside the parentheses:
1. Multiply [tex]$5x^2$[/tex] by [tex]$2x^2$[/tex]:
[tex]$$5x^2 \cdot 2x^2 = (5 \cdot 2)(x^2 \cdot x^2) = 10x^4.$$[/tex]
2. Multiply [tex]$5x^2$[/tex] by [tex]$13x$[/tex]:
[tex]$$5x^2 \cdot 13x = (5 \cdot 13)(x^2 \cdot x) = 65x^3.$$[/tex]
3. Multiply [tex]$5x^2$[/tex] by [tex]$-5$[/tex]:
[tex]$$5x^2 \cdot (-5) = 5 \cdot (-5)x^2 = -25x^2.$$[/tex]
Now, combine all the terms to get the final expanded expression:
[tex]$$10x^4 + 65x^3 - 25x^2.$$[/tex]
Thus, the answer is
[tex]$$\boxed{10x^4 + 65x^3 - 25x^2}.$$[/tex]
