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(a) Multiply out and simplify $(x + 5)(x^2 - 2x + 6)$. - Junior Cycle Mathematics - Question 7 - 2015

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(a)-Multiply-out-and-simplify-$(x-+-5)(x^2---2x-+-6)$.-Junior Cycle Mathematics-Question 7-2015.png

(a) Multiply out and simplify $(x + 5)(x^2 - 2x + 6)$.

Worked Solution & Example Answer:(a) Multiply out and simplify $(x + 5)(x^2 - 2x + 6)$. - Junior Cycle Mathematics - Question 7 - 2015

Step 1

Multiply out $(x + 5)(x^2 - 2x + 6)$

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Answer

To begin with, we will distribute each term in (x+5)(x + 5) across the polynomial (x2−2x+6)(x^2 - 2x + 6). </br> </br> First, multiply xx by each term of the polynomial: </br> x⋅x2=x3x \cdot x^2 = x^3 </br> x⋅(−2x)=−2x2x \cdot (-2x) = -2x^2 </br> x⋅6=6xx \cdot 6 = 6x </br> </br> Then, multiply 55 by each term of the polynomial: </br> 5⋅x2=5x25 \cdot x^2 = 5x^2 </br> 5⋅(−2x)=−10x5 \cdot (-2x) = -10x </br> 5⋅6=305 \cdot 6 = 30 </br> </br> Combining these results, we have:</br> x3−2x2+6x+5x2−10x+30x^3 - 2x^2 + 6x + 5x^2 - 10x + 30

Step 2

Combine like terms

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Answer

Next, combine the like terms in the expression: </br> - For the x2x^2 terms: −2x2+5x2=3x2-2x^2 + 5x^2 = 3x^2 </br> - For the xx terms: 6x−10x=−4x6x - 10x = -4x </br> </br> Therefore, we simplify this to: </br> x3+3x2−4x+30x^3 + 3x^2 - 4x + 30

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