Are the expressions on both sides equivalent?
5x2+7x+7=?(2x+3)(3x+4)
To determine if the expressions are equivalent, we need to expand the right-side expression, (2x+3)(3x+4), and compare it with 5x2+7x+7.
Let's expand the right-side expression:
- First, use the distributive property (or FOIL):
- (2x+3)(3x+4)=2x⋅3x+2x⋅4+3⋅3x+3⋅4
- This simplifies to 6x2+8x+9x+12.
- Combine like terms: 6x2+(8x+9x)+12=6x2+17x+12.
Now, compare the expanded expression 6x2+17x+12 to the left side 5x2+7x+7:
- The coefficient of x2 is 6 on the right, but 5 on the left.
- The coefficient of x is 17 on the right, but 7 on the left.
- The constant term is 12 on the right, but 7 on the left.
Since all corresponding coefficients differ between the two sides, the expressions are not equivalent.
Therefore, the correct answer is: No, because all the coefficients of the corresponding terms in the expressions on both sides of the equation are different.
No, because all the coefficients of the corresponding terms in the expressions on both sides of the equation are different.