Find the product of ( t − 6 ) ( \sqrt { t } - 6 ) ( t − 6 ) and its conjugate.A) t − 6 \sqrt { t } - 6 t − 6 B) t − 12 t- 12 t − 12 C) t − 36 \sqrt { t } - 36 t − 36 D) t − 36 t - 36 t − 36 E) t + 12 t − 36 t + 12 \sqrt { t } - 36 t + 12 t − 36

Question

Find the product of   ( t − 6 )  ( \sqrt { t } - 6 )  ( t ​ − 6 )    and its conjugate.A)    t − 6 \sqrt { t } - 6 t ​ − 6 B)    t − 12 t- 12 t − 12 C)    t − 36 \sqrt { t } - 36 t ​ − 36 D)    t − 36 t - 36 t − 36 E)    t + 12 t − 36 t + 12 \sqrt { t } - 36 t + 12 t ​ − 36

Franky freemen · Accepted Answer

Final Answer : D, Explanation :  The product of a binomial and its conjugate follows the pattern of the difference of squares, which is $(a+b)(a-b)=a^2-b^2$. In this case, the binomial is $\sqrt{t}-6$ and its conjugate is $\sqrt{t}+6$, so their product is $(\sqrt{t}-6)(\sqrt{t}+6)=\sqrt{t^2}-36=t-36$. Thus, the best choice is D.

Find the product of $\sqrt { t } - 6 )$ and its conjugate.

A) $t−6\sqrt { t } - 6$
B) $t - 12$
C) $t−36\sqrt { t } - 36$
D) $t - 36$
E) $\sqrt { t } - 36$

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Learning Objectives

Learning Objectives

Related questions

Find the product of (t−6) ( \sqrt { t } - 6 ) (t​−6) and its conjugate.A) t−6\sqrt { t } - 6t​−6 B) t−12t- 12t−12 C) t−36\sqrt { t } - 36t​−36 D) t−36t - 36t−36 E) t+12t−36t + 12 \sqrt { t } - 36t+12t​−36

Definitions

Learning Objectives

Learning Objectives

Related questions

Find the product of $\sqrt { t } - 6 )$ and its conjugate.

A) $t−6\sqrt { t } - 6$
B) $t - 12$
C) $t−36\sqrt { t } - 36$
D) $t - 36$
E) $\sqrt { t } - 36$