Question

state whether the expressions are\

1. \\(5x + 15\\) and \\(5(x + 3)\\)\
2. \\(12x - 6\\) and \\(3(4x - 3)\\)\
3. \\(40x + 4\\) and \\(4(10 + x)\\)\
4. \\(9x - 6\\) and \\(3(2 + 3x)\\)\

expand and simplify each express\

1. \\(7(2a + 5) + 2(3a + 5)\\)

Explanation:

Problem 9:

Step1: Expand \( 5(x + 3) \)

Using the distributive property \( a(b + c)=ab + ac \), we have \( 5(x + 3)=5\times x+5\times 3 = 5x+15 \)

Step2: Compare with \( 5x + 15 \)

The expanded form of \( 5(x + 3) \) is \( 5x + 15 \), which is the same as the first expression.

Step1: Expand \( 3(4x - 3) \)

Using the distributive property \( a(b - c)=ab - ac \), we get \( 3(4x - 3)=3\times4x-3\times3 = 12x - 9 \)

Step2: Compare with \( 12x - 6 \)

The expression \( 12x - 9 \) is not equal to \( 12x - 6 \) (since \(-9
eq - 6\)).

Step1: Expand \( 4(10 + x) \)

Using the distributive property \( a(b + c)=ab + ac \), we have \( 4(10 + x)=4\times10+4\times x=40 + 4x \)

Step2: Compare with \( 40x + 4 \)

The expression \( 40 + 4x \) (or \( 4x + 40 \)) is not equal to \( 40x + 4 \) (since the coefficients of \( x \) and the constant terms are different).

Answer:

The expressions \( 5x + 15 \) and \( 5(x + 3) \) are equivalent.

Problem 10: