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Expand and simplify the following binomial products using the distributive property:

Mathematics

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here are the solutions using the specified method:

2.2.1 (x+4)(x+10)(x+4)(x+10)

  1. Write the second bracket twice.

    =(x+10)(x+10)= (x+10) \quad (x+10)

  2. Distribute the first bracket over the expression in Step 1.

    =x(x+10)+4(x+10)= x(x+10) + 4(x+10)

  3. Remove the brackets.

    =x2+10x+4x+40= x^2 + 10x + 4x + 40

  4. Simplify.

    =x2+14x+40= \boxed{x^2 + 14x + 40}

    2.2.2 (x+9)(x−2)(x+9)(x-2)

  5. Write the second bracket twice.

    =(x−2)(x−2)= (x-2) \quad (x-2)

  6. Distribute the first bracket over the expression in Step 1.

    =x(x−2)+9(x−2)= x(x-2) + 9(x-2)

  7. Remove the brackets.

    =x2−2x+9x−18= x^2 - 2x + 9x - 18

  8. Simplify.

    =x2+7x−18= \boxed{x^2 + 7x - 18}
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