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Answer:

Standard form of a quadratic expression: [tex]ax^2+bx+c[/tex]

Question 1

Apply the FOIL method: [tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

[tex]\begin{aligned}\implies(2x+5)(x+1)&=2x \cdot x+2x \cdot 1+5 \cdot x+5 \cdot 1\\& = 2x^2+2x+5x+5\\ & = 2x^2+7x+5\end{aligned}[/tex]

Question 2

Apply the Difference of Two Squares Formula: [tex](a-b)(a+b)=a^2-b^2[/tex]

[tex]\begin{aligned}\implies (x-2)(x+2)& =x^2-2^2\\& = x^2-4\end{aligned}[/tex]

Or, Apply the FOIL method: [tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

[tex]\begin{aligned}\implies(x-2)(x+2) &=x \cdot x+x \cdot 2+-2 \cdot x+-2 \cdot 2\\ & =x^2+2x-2x-4\\&=x^2-4\end{aligned}[/tex]

Answer:

see explanation

Step-by-step explanation:

A quadratic expression in standard form is

ax² + bx + c ( a ≠ 0 )

1

(2x + 5)(x + 1)

each term in the second factor is multiplied by each term in the first factor , that is

2x(x + 1) + 5(x + 1) ← distribute parenthesis

= 2x² + 2x + 5x + 5 ← collect like terms

= 2x² + 7x + 5 ← in standard form

Similarly

2

(x + 2)(x - 2)

= x(x - 2) + 2(x - 2) ← distribute parenthesis

= x² - 2x + 2x - 4 ← collect like terms

= x² - 4 ← in standard form

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