Answer :
To simplify the expression \((x + 2)(2x + 5)\), we can use the distributive property (also known as the FOIL method for binomials). The steps are as follows:
1. First, multiply the first terms in each binomial:
[tex]\[ x \cdot 2x = 2x^2 \][/tex]
2. Outer, multiply the outer terms:
[tex]\[ x \cdot 5 = 5x \][/tex]
3. Inner, multiply the inner terms:
[tex]\[ 2 \cdot 2x = 4x \][/tex]
4. Last, multiply the last terms:
[tex]\[ 2 \cdot 5 = 10 \][/tex]
Next, combine all these products:
[tex]\[ 2x^2 + 5x + 4x + 10 \][/tex]
Now, combine the like terms \(5x\) and \(4x\):
[tex]\[ 2x^2 + 9x + 10 \][/tex]
Thus, the simplified expression is:
[tex]\[ 2x^2 + 9x + 10 \][/tex]
Therefore, the coefficients for the simplified expression \(2x^2 + 9x + 10\) are:
[tex]\[ \boxed{2} \][/tex]
[tex]\[ \boxed{9} \][/tex]
[tex]\[ \boxed{10} \][/tex]
1. First, multiply the first terms in each binomial:
[tex]\[ x \cdot 2x = 2x^2 \][/tex]
2. Outer, multiply the outer terms:
[tex]\[ x \cdot 5 = 5x \][/tex]
3. Inner, multiply the inner terms:
[tex]\[ 2 \cdot 2x = 4x \][/tex]
4. Last, multiply the last terms:
[tex]\[ 2 \cdot 5 = 10 \][/tex]
Next, combine all these products:
[tex]\[ 2x^2 + 5x + 4x + 10 \][/tex]
Now, combine the like terms \(5x\) and \(4x\):
[tex]\[ 2x^2 + 9x + 10 \][/tex]
Thus, the simplified expression is:
[tex]\[ 2x^2 + 9x + 10 \][/tex]
Therefore, the coefficients for the simplified expression \(2x^2 + 9x + 10\) are:
[tex]\[ \boxed{2} \][/tex]
[tex]\[ \boxed{9} \][/tex]
[tex]\[ \boxed{10} \][/tex]
