Multiply and simplify. ( 10 − 9 9 t ) ( 10 + 9 9 t ) ( 10 - 9 \sqrt { 9 t } ) ( 10 + 9 \sqrt { 9 t } ) ( 10 − 9 9 t ) ( 10 + 9 9 t ) A) 2000 − 162 t 2000 - 162 t 2000 − 162 t B) 300 − 243 t 300 - 243 t 300 − 243 t C) 1000 + 91 t 1000 + 91 t 1000 + 91 t D) 200 + 81 t 200 + 81 t 200 + 81 t E) 100 − 729 t 100 - 729 t 100 − 729 t

Question

Multiply and simplify.   ( 10 − 9 9 t )  ( 10 + 9 9 t )  ( 10 - 9 \sqrt { 9 t } )  ( 10 + 9 \sqrt { 9 t } )  ( 10 − 9 9 t ​ )  ( 10 + 9 9 t ​ )  A)    2000 − 162 t 2000 - 162 t 2000 − 162 t B)    300 − 243 t 300 - 243 t 300 − 243 t C)    1000 + 91 t 1000 + 91 t 1000 + 91 t D)    200 + 81 t 200 + 81 t 200 + 81 t E)    100 − 729 t 100 - 729 t 100 − 729 t

Logan Burkhart · Accepted Answer

Final Answer : E, Explanation :   This problem uses the difference of squares formula,   a 2 − b 2 = ( a − b ) ( a + b ) a^2 - b^2 = (a - b)(a + b) a 2 − b 2 = ( a − b ) ( a + b )  . Here,   a = 10 a = 10 a = 10   and   b = 9 9 t b = 9\sqrt{9t} b = 9 9 t ​  . Squaring   b b b   gives   81 ⋅ 9 t = 729 t 81 \cdot 9t = 729t 81 ⋅ 9 t = 729 t  . Thus, the simplified form is   1 0 2 − ( 9 9 t ) 2 = 100 − 729 t 10^2 - (9\sqrt{9t})^2 = 100 - 729t 1 0 2 − ( 9 9 t ​ ) 2 = 100 − 729 t  .

Multiply and simplify. $\sqrt { 9 t } ) ( 10 + 9 \sqrt { 9 t } )$

A) $2000 - 162 t$
B) $300 - 243 t$
C) $1000 + 91 t$
D) $200 + 81 t$
E) $100 - 729 t$

Definitions

Learning Objectives

Learning Objectives

Related questions

Multiply and simplify. (10−99t) (10+99t) ( 10 - 9 \sqrt { 9 t } ) ( 10 + 9 \sqrt { 9 t } ) (10−99t​) (10+99t​) A) 2000−162t2000 - 162 t2000−162t B) 300−243t300 - 243 t300−243t C) 1000+91t1000 + 91 t1000+91t D) 200+81t200 + 81 t200+81t E) 100−729t100 - 729 t100−729t

Definitions

Learning Objectives

Learning Objectives

Related questions

Multiply and simplify. $\sqrt { 9 t } ) ( 10 + 9 \sqrt { 9 t } )$

A) $2000 - 162 t$
B) $300 - 243 t$
C) $1000 + 91 t$
D) $200 + 81 t$
E) $100 - 729 t$