Q7 Simplify the product of
(2x - 5y^3)^2
Q8 Factor the trinomial.
g^2 + 4g - 21
Q9 Simplify and write your final answer in factored form.
(9r^3 + 2r^2 - 5r + 4) - (5r^3 - 7r + 4)
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Q7
To simplify the product of (2x - 5y^3)^2, we need to square the binomial:
(2x - 5y^3)^2 = (2x - 5y^3)(2x - 5y^3)
Expanding using the FOIL method:
= 4x^2 - 10xy^3 - 10xy^3 + 25y^6
= 4x^2 - 20xy^3 + 25y^6
Therefore, (2x - 5y^3)^2 simplifies to 4x^2 - 20xy^3 + 25y^6.
Q8
To factor the trinomial g^2 + 4g - 21, we need to find two numbers that multiply to -21 and add up to 4. The numbers are 7 and -3.
Therefore, we can factor the trinomial as:
g^2 + 4g - 21 = (g + 7)(g - 3)
Q9
To simplify (9r^3 + 2r^2 - 5r + 4) - (5r^3 - 7r + 4), we first distribute the negative sign to the second parenthesis:
= 9r^3 + 2r^2 - 5r + 4 - 5r^3 + 7r - 4
Combine like terms:
= 9r^3 - 5r^3 + 2r^2 - 5r + 7r + 4 - 4
= 4r^3 + 2r^2 + 2r
The final simplified expression in factored form is 4r^3 + 2r^2 + 2r.