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Giải câu hỏi trắc nghiệm trang 33 vở thực hành Toán 8

Chọn phương án đúng trong mỗi câu sau:

ꦕTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Lựa chọn câu để xem lời giải nhanh hơn
Chọn phương án đúng trong mỗi câu sau:

Câu 1 trang 33

Đa thức \(8{x^3} - 27{y^3}\) được viết thành tích của hai đa thức: A. \(2x + 3y\) và \(4{x^2} - 6xy + 9{y^2}\). B. \(2x + 3y\) và \(4{x^2} + 6xy + 9{y^2}\). C. \(2x-3y\) và \(4{x^2} - 6xy + 9{y^2}\). D. \(2x-3y\) và \(4{x^2} + 6xy + 9{y^2}\).

Phương pháp giải:

🦩Sử dụng hằng đẳng thức hiệu hai lập phương: \({a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)\)

Lời giải chi tiết:

Ta có \(8{x^3} - 27{y^3} = \left( {2x - 3y} \right)\left( {4{x^2} + 6xy + 9{y^2}} \right).\) => Chọn đáp án D.

Câu 2 trang 33

Đa thức \({x^3} + 8{y^3}\) được viết thành tích của hai đa thức: A. \(x + 2y\) và \({x^2} + 2xy + 4{y^2}\). B. \(x + 2y\) và \({x^2} - 2xy + 4{y^2}\). C. \(x - 2y\) và \({x^2} - 2xy + 4{y^2}\). D. \(x - 2y\) và \({x^2} + 2xy + 4{y^2}\).

Phương pháp giải:

ꦗSử dụng hằng đẳng thức tổng hai lập phương: \({a^3} + {b^3} = (a + b)\left( {{a^2} - ab + {b^2}} \right)\)

Lời giải chi tiết:

Ta có \({x^3} + 8{y^3} = \left( {x + 2y} \right)\left( {{x^2} - 2xy + 4{y^2}} \right).\) => Chọn đáp án B.

Câu 3 trang 33

Biểu thức \(\left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right) - \left( {x + 2} \right)\left( {{x^2} - 2x + 4} \right)\) được rút gọn thành A. \( - 16\). B. \(16\). C. \(2{x^3}\). D. \( - 2{x^3}\).

Phương pháp giải:

𓆉- Sử dụng hằng đẳng thức tổng hai lập phương: \({a^3} + {b^3} = (a + b)\left( {{a^2} - ab + {b^2}} \right)\)

🦄- Sử dụng hằng đẳng thức hiệu hai lập phương: \({a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)\)

Lời giải chi tiết:

Ta có \((x - 2)({x^2} + 2x + 4) - (x + 2)({x^2} - 2x + 4)\) \(\begin{array}{l} = \left( {{x^3} - {2^3}} \right) - \left( {{x^3} + {2^3}} \right)\\ = {x^3} - 8 - {x^3} - 8 =  - 16.\end{array}\) => Chọn đáp án A.

Câu 4 trang 33

Khẳng định nào sau đây là đúng? A. \({A^3} + {B^3} = (A - B)({A^2} + AB + {B^2})\). B. \({A^3} + {B^3} = (A + B)({A^2} + AB + {B^2})\). C. \({A^3} - {B^3} = (A - B)({A^2} - AB + {B^2})\). D. \({A^3} - {B^3} = (A - B)({A^2} + AB + {B^2})\).

Phương pháp giải:

ꦐ- Sử dụng hằng đẳng thức tổng hai lập phương: \({a^3} + {b^3} = (a + b)\left( {{a^2} - ab + {b^2}} \right)\)

♔- Sử dụng hằng đẳng thức hiệu hai lập phương: \({a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)\)

Lời giải chi tiết:

Khẳng định đúng là \({A^3} - {B^3} = \left( {A - B} \right)\left( {{A^2} + AB + {B^2}} \right).\) => Chọn đáp án D.

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