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Multiply [tex]5x^2(2x^2 + 13x - 5)[/tex].

A. [tex]10x^4 + 65x^3 - 25x^2[/tex]
B. [tex]10x^2 + 65x - 25[/tex]
C. [tex]7x^4 + 18x^3 - 10x^2[/tex]
D. [tex]7x^2 + 18x - 10[/tex]

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]

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