Chapter 5: Problem 9

Simplify, if possible, (a) \((9 x)(-3 y)\) (b) \(9(4 x+5 x)\) (c) \(-2 x+11 x\) (d) \((-2 x)(11 x)\) (e) \(3 x-2 y+4 z-2 x-3 y+9 z\) (f) \((8 m)(-3 q)\) (g) \(8 m(-3 q)\) (h) \(8 m-3 q\) (i) \(8(m-3 q)\) (k) \(\frac{8 a b^{2} d}{4 a b c}\) (1) \(x-x(\mathrm{~m})(x)(-x)\) (n) \(x(-x)\) (o) \(-x(x)\)

Short Answer

Expert verified

Question: Simplify the following expression: \(9(4 x+5 x)\) Answer: \(81x\)

Step by step solution

Expression (a)

Simplify \((9 x)(-3 y)\). To do this, we simply multiply the constants, and then multiply the variables, like so: \((9 x)(-3 y) = (9)(-3)(x)(y)=-27xy\).

Expression (b)

Simplify \(9(4 x+5 x)\). First, we will apply the distributive property by multiplying the constant by each of the terms inside the parentheses: \(9(4 x+5 x) = (9)(4 x) + (9)(5 x)\). Then, multiply the constants with the variables: \((36x) + (45x)\). Finally, combine like terms: \(36x + 45x = 81x\).

Expression (c)

Simplify \(-2 x+11 x\). To do this, simply add the coefficients of the like terms \(-2x\) and \(11x\): \(-2 x+11 x = 9x\).

Expression (d)

Simplify \((-2 x)(11 x)\). To do this, multiply the constants and multiply the variables: \((-2 x)(11 x) = (-2)(11)(x)(x)=-22x^2\).

Expression (e)

Simplify \(3 x-2 y+4 z-2 x-3 y+9 z\). Combine like terms by adding or subtracting their coefficients: \((3x-2x)+(-2y-3y)+(4z+9z)\). This simplifies to \(1x-5y+13z\), or \(x-5y+13z\).

Expression (f)

Simplify \((8 m)(-3 q)\). Multiply the constants, and then multiply the variables: \((8 m)(-3 q) = (-24)(m)(q)=-24mq\).

Expression (g)

Since this expression is identical to expression (f), the solution is the same: \(8m(-3q)=-24mq\).

Expression (h)

This expression is already simplified, as there are no like terms to combine: \(8m - 3q\).

Expression (i)

Simplify \(8(m-3q)\). Apply the distributive property by multiplying the constant by each of the terms inside the parentheses: \(8(m-3q) = (8)(m) - (8)(3q)\). Multiply the constants with their respective variables: \(8m - 24q\).

Expression (k)

Simplify \(\frac{8ab^2d}{4abc}\). First, cancel out the common factors of the numerator and denominator: \(\frac{2ab^2d}{bc}\). This cannot be further simplified.

Expression (l)

Simplify \(x-x+mx(x)(-x)\). The first two terms, \(x-x\), cancel out, leaving \(mx(x)(-x)\). This can be simplified by multiplying the variables: \(mx(-x^2)\).

Expression (n)

Simplify \(x(-x)\). Multiply the variables: \(x(-x) = -x^2\).

Expression (o)

This expression is the same as expression (n), so the solution is the same: \(-x(x)=-x^2\).

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Simplify, if possible, (a) \((9 x)(-3 y)\) (b) \(9(4 x+5 x)\) (c) \(-2 x+11 x\) (d) \((-2 x)(11 x)\) (e) \(3 x-2 y+4 z-2 x-3 y+9 z\) (f) \((8 m)(-3 q)\) (g) \(8 m(-3 q)\) (h) \(8 m-3 q\) (i) \(8(m-3 q)\) (k) \(\frac{8 a b^{2} d}{4 a b c}\) (1) \(x-x(\mathrm{~m})(x)(-x)\) (n) \(x(-x)\) (o) \(-x(x)\)

Short Answer

Step by step solution

Expression (a)

Expression (b)

Expression (c)

Expression (d)

Expression (e)

Expression (f)

Expression (g)

Expression (h)

Expression (i)

Expression (k)

Expression (l)

Expression (n)

Expression (o)

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