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1. Use suitable identities to find the following product:

(i) [tex]\((3x + 4)(3x - 5)\)[/tex]


Sagot :

To find the product [tex]\( (3x + 4)(3x - 5) \)[/tex] using suitable identities, we can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last) for multiplying two binomials. Let's go through this step-by-step:

1. First: Multiply the first terms of each binomial:
[tex]\[ 3x \times 3x = 9x^2 \][/tex]

2. Outer: Multiply the outer terms of each binomial:
[tex]\[ 3x \times (-5) = -15x \][/tex]

3. Inner: Multiply the inner terms of each binomial:
[tex]\[ 4 \times 3x = 12x \][/tex]

4. Last: Multiply the last terms of each binomial:
[tex]\[ 4 \times (-5) = -20 \][/tex]

5. Now, combine all the products:
[tex]\[ 9x^2 + (-15x) + 12x + (-20) \][/tex]

6. Simplify the expression by combining like terms:
[tex]\[ 9x^2 - 15x + 12x - 20 \][/tex]

7. Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 9x^2 - 3x - 20 \][/tex]

Therefore, the product of [tex]\( (3x + 4)(3x - 5) \)[/tex] is:
[tex]\[ 9x^2 - 3x - 20 \][/tex]