which expression has an equivalent value to $x^{2}+9x + 8$ for all values of $x$?\n$(x + 1)(x + 8)$\n$(x +…

which expression has an equivalent value to $x^{2}+9x + 8$ for all values of $x$?\n$(x + 1)(x + 8)$\n$(x + 2)(x + 6)$\n$(x + 4)(x + 4)$\n$(x + 5)(x + 4)$

which expression has an equivalent value to $x^{2}+9x + 8$ for all values of $x$?\n$(x + 1)(x + 8)$\n$(x + 2)(x + 6)$\n$(x + 4)(x + 4)$\n$(x + 5)(x + 4)$

Answer

Explanation:

Step1: Expand each option

Use FOIL method (First - Outer - Inner - Last). For option A: $(x + 1)(x + 8)=x\times x+x\times8+1\times x + 1\times8=x^{2}+8x+x + 8=x^{2}+9x + 8$. For option B: $(x + 2)(x + 6)=x\times x+x\times6+2\times x+2\times6=x^{2}+6x+2x + 12=x^{2}+8x + 12$. For option C: $(x + 4)(x + 4)=x\times x+x\times4+4\times x+4\times4=x^{2}+4x+4x + 16=x^{2}+8x + 16$. For option D: $(x + 5)(x + 4)=x\times x+x\times4+5\times x+5\times4=x^{2}+4x+5x + 20=x^{2}+9x + 20$.

Answer:

A. $(x + 1)(x + 8)$