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1 December, 09:46

Simplify the expression $x - 2 (1+x) + 3 (1-x) - 4 (1+2x) $.

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  1. 1 December, 10:04
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    Answer:see below

    Step-by-step explanation:

    1+x evaluates to 1+x

    Multiply 2 by 1+x

    we multiply 2 by each term in 1+x term by term.

    This is the distributive property of multiplication.

    Multiply 2 and 1

    1

    2 * 1 = 2

    Multiply 2 and x

    Multiply 1 and x

    The x just gets copied along.

    x

    2 * x = 2x

    2 * (1+x) evaluates to 2+2x

    x - 2x = - x

    The answer is - x-2

    x-2 * (1+x) evaluates to - x-2

    1-x evaluates to 1-x

    Multiply 3 by 1-x

    we multiply 3 by each term in 1-x term by term.

    This is the distributive property of multiplication.

    Multiply 3 and 1

    1

    3 * 1 = 3

    Multiply 3 and - x

    Multiply 1 and x

    The x just gets copied along.

    x

    3 * - x = - 3x

    3 * (1-x) evaluates to 3-3x

    To add the polynomials - x-2 and 3-3x we try to add or combine terms in one polynomialwith any like terms in the other polynomial.

    -x + - 3x = - 4x

    -2 + 3 = 1

    The answer is - 4x+1

    x-2 * (1+x) + 3 * (1-x) evaluates to - 4x+1

    Multiply x and 2

    Multiply x and 1

    The x just gets copied along.

    The answer is x

    x

    2*x evaluates to 2x

    1+2*x evaluates to 1+2x

    Multiply 4 by 1+2x

    we multiply 4 by each term in 1+2x term by term.

    This is the distributive property of multiplication.

    Multiply 4 and 1

    1

    4 * 1 = 4

    Multiply 4 and 2x

    Multiply 1 and x

    The x just gets copied along.

    x

    4 * 2x = 8x

    4 * (1+2*x) evaluates to 4+8x

    To subtract the polynomials - 4x+1 and 4+8x we try to subtract terms in one polynomialwith any like terms in the other polynomial.

    Be very careful with the "-" sign in front of 4+8x it is to be used on all terms in it.

    -4x - 8x = - 12x

    1 - 4 = - 3

    The answer is - 12x-3

    x-2 * (1+x) + 3 * (1-x) - 4 * (1+2*x) evaluates to - 12x-3

    The final answer is

    -12x-3
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