Question

Which expressions are equivalent to 10a - 25 + 5b

−2(−5a−25+5b)
(2a−5+b)5
10×(a−2.5+0.5b)
(−2a+5−b)⋅(−5)
−10⋅(−a−2.5−0.5b)

Answer 1

(2a − 5 + b) · 5

10×(a − 2.5 + 0.5b)

(−2a + 5 − b) ⋅ (−5)

Explanation:

`10a-25+5b\\\\-2(-5a-25+5b)=(-2)(-5a)+(-2)(-25)+(-2)(5b)\\=10a+50-10b\qquad NOT\\\\(2a-5+b)(5)=(2a)(5)+(-5)(5)+(b)(5)=10a-25+5b\qquad YES\\\\10(a-2.5+0.5b)=(10)(a)+(10)(-2.5)+(10)(0.5b)\\=10a-25+5b\qquad YES\\\\(-2a+5-b)(-5)=(-2a)(-5)+(5)(-5)+(-b)(-5)\\=10a-25+5b\qquad YES\\\\-10(-a-2.5-0.5b)=(-10)(-a)+(-10)(-2.5)+(-10)(-0.5b)\\=10a+25+5b\qquad NOT`