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Sagot :
Let's solve for the product of the binomials [tex]\((2x + 5)(3x - 4)\)[/tex] using the distributive property, often referred to as the FOIL method for binomials.
Step 1: Expand the product using the distributive property
[tex]\[ (2x + 5)(3x - 4) \][/tex]
[tex]\[ = (2x \cdot 3x) + (2x \cdot -4) + (5 \cdot 3x) + (5 \cdot -4) \][/tex]
Step 2: Multiply each term
1. Multiply the first terms:
[tex]\[ 2x \cdot 3x = 6x^2 \][/tex]
2. Multiply the outer terms:
[tex]\[ 2x \cdot -4 = -8x \][/tex]
3. Multiply the inner terms:
[tex]\[ 5 \cdot 3x = 15x \][/tex]
4. Multiply the last terms:
[tex]\[ 5 \cdot -4 = -20 \][/tex]
Step 3: Combine like terms
Now, combine the terms we obtained:
[tex]\[ 6x^2 - 8x + 15x - 20 \][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[ -8x + 15x = 7x \][/tex]
Step 4: Write the final expression
[tex]\[ 6x^2 + 7x - 20 \][/tex]
So, the product of the binomials [tex]\((2x + 5)(3x - 4)\)[/tex] is:
[tex]\[ 6x^2 + 7x - 20 \][/tex]
Step 1: Expand the product using the distributive property
[tex]\[ (2x + 5)(3x - 4) \][/tex]
[tex]\[ = (2x \cdot 3x) + (2x \cdot -4) + (5 \cdot 3x) + (5 \cdot -4) \][/tex]
Step 2: Multiply each term
1. Multiply the first terms:
[tex]\[ 2x \cdot 3x = 6x^2 \][/tex]
2. Multiply the outer terms:
[tex]\[ 2x \cdot -4 = -8x \][/tex]
3. Multiply the inner terms:
[tex]\[ 5 \cdot 3x = 15x \][/tex]
4. Multiply the last terms:
[tex]\[ 5 \cdot -4 = -20 \][/tex]
Step 3: Combine like terms
Now, combine the terms we obtained:
[tex]\[ 6x^2 - 8x + 15x - 20 \][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[ -8x + 15x = 7x \][/tex]
Step 4: Write the final expression
[tex]\[ 6x^2 + 7x - 20 \][/tex]
So, the product of the binomials [tex]\((2x + 5)(3x - 4)\)[/tex] is:
[tex]\[ 6x^2 + 7x - 20 \][/tex]
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