Is my answer correct here?
(5x²-5) multiply by (2x²+3x-15)
is equals to 10x⁴+15x³-10x²-15x
Answer (1)
The answer is incorrect.1. Distribute [tex]$$(5x^{2} - 5)$$[/tex] across [tex]$$(2x^{2} + 3x - 15)$$[/tex] We will apply the distributive property (also known as the FOIL method for binomials) to multiply the two polynomials.The expression can be expanded as follows: [tex]$$(5x^{2})(2x^{2}) + (5x^{2})(3x) + (5x^{2})(-15) + (-5)(2x^{2}) + (-5)(3x) + (-5)(-15)$$[/tex] 2. Calculate each term.[tex]$$(5x^{2})(2x^{2}) = 10x^{4}$$[/tex][tex]$$(5x^{2})(3x) = 15x^{3}$$[/tex][tex]$$(5x^{2})(-15) = -75x^{2}$$[/tex][tex]$$(-5)(2x^{2}) = -10x^{2}$$[/tex][tex]$$(-5)(3x) = -15x$$[/tex][tex]$$(-5)(-15) = 75$$[/tex]Combine all the terms.Now, we combine the results from[tex]$$10x^{4} + 15x^{3} - 75x^{2} - 10x^{2} - 15x + 75$$[/tex]3. Combine like terms.Combine the [tex]$$x^{2}$$[/tex] terms:[tex]$$-75x^{2} - 10x^{2} = -85x^{2}$$[/tex]Thus, the final expression is:[tex]$$10x^{4} + 15x^{3} - 85x^{2} - 15x + 75$$[/tex]Now, let's compare this with the provided answer [tex]$$10x^{4} + 15x^{3} - 10x^{2} - 15x$$[/tex] The provided answer is missing the constant term [tex]$$+75$$[/tex] and has incorrect coefficients for the [tex]$$x^{2}$$[/tex] term.Therefore, the answer given is incorrect.
