Question

Multiply or divide, as indicated. (xz - xw + 2yz - 2yw)/(z2 - w2) * (4z + 4w + xz + wx)/(16 - x2)

Accepted Answer

Start by examining the given expression: $$\frac{(xz - xw + 2yz - 2yw)}{(z^2$ - w^2$)} 	imes \frac{(4z + 4w + xz + wx)}{(16 - x^2$)}. $$Look for common factoring opportunities in each part of the expression. For the numerator of the first fraction, group terms to factor by grouping: $$xz - xw + 2yz - 2yw = (xz - xw) + (2yz - 2yw). $$Factor out common factors from each group: $$x(z - w) + 2y(z - w)$$, then factor out the common binomial $$(z - w) to $$get $$(x + 2y)(z - w). $$Factor the denominator of the first fraction, $$z^2$$ - $$w^2$$, recognizing it as a difference of squares: $$z^2$$ - $$w^2 = (z - w)(z + w$$)$$. Repeat the factoring process for the second fraction: factor the numerator 4z + 4w + xz + wx$ by grouping as (4z + 4w) + (xz + wx$$)$$, then factor out common terms to get 4(z + w) + x(z + w$$)$$, which factors to (4 + x)(z + w$$)$$. For the denominator 16$$ - $$x^2$$, recognize it as a difference of squares: $$(4 - x)(4 + x).$$

Multiply or divide, as indicated. (xz - xw + 2yz - 2yw)/(z² - w²) * (4z + 4w + xz + wx)/(16 - x²)

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Key Concepts

Factoring Polynomials

Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions