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Expand the following expressions and simplify:

Mathematics

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Answer

10m2+6mn−4n210m^2 + 6mn - 4n^2

Step-by-step solution

5 steps

To expand and simplify the expression (m+n)(10m−4n)(m+n)(10m-4n), we use the distributive property (FOIL method).

  1. Multiply the first terms in each parenthesis.

    m×10m=10m2m \times 10m = 10m^2

  2. Multiply the outer terms.

    m×(−4n)=−4mnm \times (-4n) = -4mn

  3. Multiply the inner terms.

    n×10m=10mnn \times 10m = 10mn

  4. Multiply the last terms in each parenthesis.

    n×(−4n)=−4n2n \times (-4n) = -4n^2

  5. Combine all the terms and simplify by combining like terms.

    10m2−4mn+10mn−4n210m^2 - 4mn + 10mn - 4n^2 10m2+(10mn−4mn)−4n210m^2 + (10mn - 4mn) - 4n^2 10m2+6mn−4n210m^2 + 6mn - 4n^2
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