Question

2 write each of the following binomials as an equivalent product of conjugates.
(a) $x^2 - 16$
$(x+4)(x-4)$
(b) $x^2 - 100$
$(x+10)(x-10)$
(c) $x^2 - 1$
$(x+1)(x-1)$
(d) $x^2 - 25$
$(x+5)(x-5)$
(e) $4 - x^2$
$(2+x)(2-x)$

Explanation:

Step1: Recognize difference of squares

Recall $a^2-b^2=(a+b)(a-b)$

Step2: Factor (b) $x^2-100$

$x^2-100 = x^2-10^2=(x+10)(x-10)$

Step3: Factor (c) $x^2-1$

$x^2-1 = x^2-1^2=(x+1)(x-1)$

Step4: Factor (d) $x^2-25$

$x^2-25 = x^2-5^2=(x+5)(x-5)$

Step5: Factor (e) $4-x^2$

$4-x^2 = 2^2-x^2=(2+x)(2-x)$

Step1 (a): Factor $x^2-16$

$x^2-16 = x^2-4^2=(x+4)(x-4)$

Answer:

(a) $(x+4)(x-4)$
(b) $(x+10)(x-10)$
(c) $(x+1)(x-1)$
(d) $(x+5)(x-5)$
(e) $(2+x)(2-x)$