Maths · Real-valued functions, algebra of functions
Simplify (c-2 d)+(a- \) (\boldsymbol{2} \boldsymbol{c}+\boldsymbol{3} \boldsymbo
Simplify \( (2 a+b)(c-2 d)+(a- \) \( \boldsymbol{b})(\boldsymbol{2} \boldsymbol{c}+\boldsymbol{3} \boldsymbol{d})+\boldsymbol{4}(\boldsymbol{a} \boldsymbol{c}+\boldsymbol{b} \boldsymbol{d}) \)
- A. \( 8 a d+a c b-c-b d \)
- B. \( 8 a c-a d-b c-b d \)
- C. \( 8 c-a d+b c-d \)
- D. \( 8 a c+a d-b c d \)
Step-by-step solution
Expand each term: (2a+b)(c-2d)=2ac-4ad+bc-2bd; (a-b)(2c+3d)=2ac+3ad-2bc-3bd; 4(ac+bd)=4ac+4bd. Summing gives 8ac - ad - bc - bd, which matches option B.