FOIL • Perfect squares • Write the factor twice
FOIL / distribute
Multiply every term in the first binomial by every term in the second.
$$(x+3)(x-8)=x^2-8x+3x-24$$
Combine like terms.
$$x^2-5x-24$$
A square means two copies
\((x+7)^2\) is not \(x^2+49\). Write the binomial twice, then multiply.
$$(x+7)^2=(x+7)(x+7)$$
$$x^2+14x+49$$
Two different binomials. Use FOIL.
Multiply. \( (x+5)(x-2) \)
\(x^2-2x+5x-10\)
Combine like terms.
Answer: \(x^2+3x-10\)
Multiply. \( (x-4)(x+9) \)
\(x^2+9x-4x-36\)
Combine like terms.
Answer: \(x^2+5x-36\)
A square means write the binomial twice. The answer is not just first-squared plus last-squared.
Expand. \( (x+4)^2 \)
\((x+4)^2=(x+4)(x+4)\)
\(x^2+4x+4x+16\)
Combine like terms.
Answer: \(x^2+8x+16\)
Expand. \( (x-6)^2 \)
\((x-6)^2=(x-6)(x-6)\)
\(x^2-6x-6x+36\)
Combine like terms.
Answer: \(x^2-12x+36\)
Same pattern, with letters. Keep the middle term \(2ab\).
Expand. \( (x-b)^2 \)
\((x-b)^2=(x-b)(x-b)\)
\(x^2-bx-bx+b^2\)
Combine like terms.
Answer: \(x^2-2bx+b^2\)
Expand. \( (x+3a)^2 \)
\((x+3a)^2=(x+3a)(x+3a)\)
\(x^2+3ax+3ax+9a^2\)
Combine like terms.
Answer: \(x^2+6ax+9a^2\)
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